A piece of wood is designed in the shape of a cone. A cylindrical hole of radius 4cm and 2cm has been drilled into the base. The surface area of the piece of wood has to be painted, except from the area inside the hole work out the surface area to be painted give your answer in the terms of pi thank you
Answers
Answer:
= 80πcm²
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
Given the information:
Diameter of base = 12cm => its radius is: 6 cm Radius of hole = 4cmThe height: 8 cm=> Area of base = π(6²) = 36π cm²
=> Area of the hole = πr² = π(4²) = 16πcm²
As we know that, the surface area of the piece of wood has to be painted at base:
= Base area - area of hole
= 36π cm² - 16πcm²
= 20πcm²
For the curved surface area can be determined by the following formula:
Area = πrl where l is the slant height
Applying Pythagoras theorem, we have:
[tex]l^{2} = r^{2} + h^{2}[/tex]
<=> [tex]l^{2} = 6^{2} + 8^{2}[/tex]
<=> [tex]l^{2} =100[/tex]
<=> l =10
=> the curved surface area is: π*6*10 =60πcm²
Hence the total surface area to be painted is
= the curved surface area + he surface area of the piece of wood has to be painted at base
= 60πcm² +20πcm²
= 80πcm²
Hope it will find you well.
To find the surface area to be painted, calculate the total surface area of the cone and subtract the area of the cylindrical hole.
Explanation:To find the surface area to be painted, we need to calculate the total surface area of the cone and then subtract the area of the cylindrical hole.
The total surface area of a cone is given by the formula A = πr(r + l), where r is the radius of the base and l is the slant height.
In this case, the radius of the cone is the same as the radius of the base of the hole, which is 4 cm. We need to find the slant height of the cone, l.
By applying the Pythagorean theorem to the right triangle formed by the height of the cone, the slant height, and the radius of the cone, we can calculate the slant height as l = sqrt( h^2 + 4^2 ), where h is the height of the cone.
Since the height of the cone is not given, we will not be able to find the exact value for the surface area to be painted. However, we can provide the general formula based on the given information:
Surface area to be painted = (π * r1 * (r1 + sqrt( h^2 + r1^2 ))) - (2 * π * r2 * h),
where r1 is the radius of the base of the hole and r2 is the smaller radius of the hole.
Learn more about Calculating surface area of a cone with a cylindrical hole here:https://brainly.com/question/31403273
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Related Questions
HELP WILL MARK BRAINLIEST!!
A jar contains 5 red, 4 blue, and 3 yellow marbles. What is the probability of pulling a red marble, then pulling a blue marble, without replacement? Calculate to the nearest tenth.
Answers
Final answer:
The probability of pulling a red marble, then pulling a blue marble without replacement is approximately 0.114.
Explanation:
To calculate the probability of pulling a red marble, then pulling a blue marble without replacement, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The number of red marbles is 5, and the number of blue marbles is 4. When the first marble is pulled, there are a total of 12 marbles. So, the probability of pulling a red marble on the first draw is 5/12.
After pulling out a red marble, the number of blue marbles becomes 3. So, the probability of pulling a blue marble on the second draw is 3/11.
To calculate the overall probability, we multiply the probabilities of each event:
P(Red and then Blue) = P(Red) × P(Blue | Red) = 5/12 × 3/11 ≈ 0.114
Final answer:
The probability of drawing a yellow marble and then a green marble without replacement is 0.1.
Explanation:
The probability of drawing a yellow marble and then a green marble without replacement is calculated as follows:
Calculate the probability of drawing a yellow marble first: 2/9 (2 yellow marbles out of a total of 9 marbles).
Now, after drawing a yellow marble, there are 8 marbles left. Calculate the probability of drawing a green marble next: 4/8 (4 green marbles out of the remaining 8).
Multiply the two probabilities: (2/9) * (4/8) = 1/9 = 0.1111 (rounded to the nearest tenth).
You are taking a multiple-choice test that has 7 questions. Each of the questions has 5 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions? Use the Fundamental Counting Principle with three or more groups of items.
Answers
Answer:
You should be able to answer the question in 35 different ways.
Step-by-step explanation:
5 * 7 = 35
That's how I see it.
Final answer:
Using the Fundamental Counting Principle, there are [tex]5^7[/tex] or 78,125 ways to answer a 7-question multiple-choice test where each question has 5 answer choices.
Explanation:
To determine the number of ways you can answer a multiple-choice test with 7 questions, where each question has 5 answer choices, you can use the Fundamental Counting Principle. This principle states that if there are n ways to do something and m ways to do another thing, then there are n*m ways to do both things.
In this case, for each of the 7 questions, you have 5 possible answers. So, the number of ways to answer all questions is 5 * 5 * 5 * 5 * 5 * 5 * 5, or [tex]5^7[/tex]. Therefore, there are 78,125 ways to answer the 7 questions on the test.
Circle O has radius 3. Points M and N lie on circle O, and mZMON is 58
degrees. What is the length of arc MN in radians?
Answers
Find attached to the question, a hand drawn diagram of the circle.
Complete Question
Circle O has radius 3. Points M and N lie on circle O, and mMON is 58
degrees. What is the length of arc MN in radians?
Answer:
The length of arc MN in radians is 3.03687 radians.
Step-by-step explanation:
The formula for arc length =
s = rѲ
Where = = Arc length
r = radius
Ѳ = central angle in degree
In the question we were given the following values
r = radius = 3 units
Ѳ = central angle in degree = 58°
We were told to calculate arc length in radians
Therefore, we would convert 58° to radians using the formula
Degree × π/180
= 58 × π /180
= 1.012 radians.
Therefore, Arc length in radians =
S = rѲ
S = 3 × 1.0122909662 radians
= 3.0368728985 radians.
Approximately = 3.03687 radians.
Therefore, the length of arc MN in radians is 3.03687 radians.
Find the volume of the triangular prism 3cm 4 cm 5cm 11cm
Answers
To find the volume of a triangular prism, multiply the base area by the height. The formula for the volume of a prism is V = base area x height. In this case, the base is a triangle, so calculate the area using the formula for the area of a triangle. Substitute the values and multiply the base area by the height to find the volume.
Explanation:To find the volume of a triangular prism, we need to multiply the base area by the height. The formula for the volume of a prism is:
V = base area x height
In this case, the base of the prism is a triangle, so we calculate the area using the formula for the area of a triangle:
area = (base x height) / 2
Substituting the given measurements, we have:
base = 3 cm, height = 4 cm, height of prism = 11 cm
First, find the area of the triangle: area = (3 cm x 4 cm) / 2 = 6 cm².
Then, multiply the base area by the height of the prism: volume = 6 cm² x 11 cm = 66 cm³.
A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.
What is the y-intercept
Answers
We have been given that a line [tex]y=mx+b[/tex] passes through the point (10, 3) and is parallel to the line [tex]2x+5y=12[/tex]. We are asked to find the y-intercept of the line.
First of all we will rewrite our given equation in slope-intercept form as:
[tex]2x-2x+5y=12-2x[/tex]
[tex]5y=-2x+12[/tex]
[tex]\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}[/tex]
[tex]y=-\frac{2}{5}x+\frac{12}{5}[/tex]
We know that slope of parallel lines is equal, so slope of parallel line to our given line would be [tex]-\frac{2}{5}[/tex].
Now we will use slope-intercept form of equation to find y-intercept.
[tex]y=mx+b[/tex], where,
m = Slope,
b = The y-intercept.
Let us substitute [tex]m=-\frac{2}{5}[/tex] and coordinates of point [tex](10,3)[/tex] in above equation as:
[tex]3=-\frac{2}{5}(10)+b[/tex]
[tex]3=-2(2)+b[/tex]
[tex]3=-4+b[/tex]
[tex]3+4=-4+4+b[/tex]
[tex]7=b[/tex]
Therefore, the y-intercept is 7 and our required equation would be [tex]y=-\frac{2}{5}x+7[/tex].
You bike 4 miles the first day of your training, 4.2 miles the second day, 4.6 miles the third day, and 5.4 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day?
Answers
On the seventh day, following the pattern of doubling the increment from the previous day, the biker would bike 16.6 miles.
To determine how many miles will be biked on the seventh day, we need to recognize the pattern in the distances biked each day. Starting with the first day and continuing through the fourth day, we see increases of 0.2 miles, 0.4 miles, and 0.8 miles respectively. It seems that each day, the increment from the previous day doubles.
Day 1: 4 milesDay 2: 4 + 0.2 = 4.2 milesDay 3: 4.2 + 0.4 = 4.6 milesDay 4: 4.6 + 0.8 = 5.4 milesFollowing this pattern, the distances for the next three days would be:
Day 5: 5.4 + 1.6 (double of 0.8) = 7 milesDay 6: 7 + 3.2 (double of 1.6) = 10.2 milesDay 7: 10.2 + 6.4 (double of 3.2) = 16.6 milesTherefore, the biker would bike 16.6 miles on the seventh day of training following this pattern.
Consider the quadratic function f(x) = - 2x ^ 2 + 5x - 4 The leading coefficient of the function is
Answers
Answer:
{-2 is the leading coefficient of the quadratic equation }f(x)=-2x^2+5x-4
Step-by-step explanation:
Given the quadratic function
we have to find the leading coefficient of given quadratic equation.
The coefficient of x2 i.e a is known as the leading coefficient.
Comparing given equation with the standard equation, we get
a=-2
6/3 + - 1/6 Please help guys!
Answers
Answer:
11/6
Step-by-step explanation:
(17-2) Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answers
Answer:
221
Step-by-step explanation:
How many times greater is 1,000,000 than 1,000?that is how many groups of 1 thousand are there in 1 million
Answers
1,000,000 is 1,000 times greater then 1,000
Step-by-step explanation:
If you multiply 1,000x1,000 you'll get an answer of 1,000,000
Therefore, 1,000,000 is going to be 1,000 times greater
A 50 lb bag of flour costs $27. How much does 8 lbs of flour cost? Use a proportion to solve.
Answers
Answer:
$4.32
Step-by-step explanation:
We want to write a proportion to solve
50 lbs 8 lbs
----------- = --------- -----
27 dollars x dollars
Using cross products
50x = 8*27
50x=216
Divide each side by 50
50x/50 = 216/50
x=4.32
Answer:
$4.32
Step-by-step explanation:
Make a proportion using this setup:
pounds/cost=pounds/cost
A 50 pound bag costs $27, and a 8 pound bag costs $x
50 lb/$27=8 lb/$x
50/27=8/x
Cross multiply
50*x=27*8
50x=216
We want to find what a 8 pound bag, will cost (x). To do this, we need to get x by itself.
Since x and 50 are being multiplied, divide both sides by 50
50x/50=216/50
x=216/50
x=4.32
A 8 pound bag of flour will cost $4.32
Which point lies on the circle represented by the equation (x + 7)2 + (y − 10)2 = 132?
Answers
Answer:
2x+2y=128
Step-by-step explanation:
multiply X by 2 then by 7 + 2 multiply by y and7 after getting whole numbers minus from 132 and add
write 7x^2-4+6x^3-4x-x^4 in standard form
Answers
Answer:
8+24x^8
Step-by-step explanation:
Final answer:
The polynomial in standard form is –x⁴ + 6x³ + 7x² – 4x – 4, with terms ordered from the highest degree to the lowest degree.
Explanation:
To write the polynomial 7x²-4+6x³-4x-x⁴ in standard form, we need to arrange the terms in descending order of their exponents. The standard form for a polynomial is to start with the highest degree term and go down to the constant term.
So, the polynomial in standard form will be:
-x⁴ + 6x³ + 7x² - 4x - 4.
This polynomial is now in the proper order and ready to be used for further algebraic operations such as factoring or solving for specific values of x.
Sharla invests $275 in a simple interest bearing account for 16 years. The annual interest rate is 8%. Using the simple interest formula, I = P r t, how much interest will Sharla’s initial investment earn over the 16 year period?
Answers
Answer:
Step-by-step explanation:
P = $ 275
r = 8% = 8/100
t = 16 years
[tex]I=275*\frac{8}{100}*16\\\\I=\frac{35200}{100}\\I=352[/tex]
I =$352
Answer:
352
Explaning:
Lamonting
Alex is on vacation and has the clothes listed above with her she's trying to pick out an outfit what is the probability she chooses a redshirt in
Answers
Answer:
The answer is 0.33.
trust me =)
A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is compounded quarterly.
Answers
Answer:
Effective annual yield = 0.05094534 or 5.094%
Step-by-step explanation:
Given:
Rate of interest (r) = 5% = 0.05
Interest = compounded quarterly
Find:
Effective annual yield = Y
Computation:
[tex]Y=(1+\frac{r}{n} )^n-1\\\\Y=(1+\frac{0.05}{4} )^4-1\\\\Y=(1+0.0125 )^4-1\\\\Y=(1.0125 )^4-1\\\\ Y=1.05094534-1\\\\Y=0.05094534\\\\\\[/tex]
Effective annual yield = 0.05094534 or 5.094%
The effective annual yield of a 5% interest rate compounded quarterly is calculated to be approximately 5.1%.
To find the effective annual yield of a passbook savings account with a rate of 5% compounded quarterly, follow these steps:
Identify the nominal interest rate and the compounding periods per year:
Nominal rate (r ): 5% or 0.05,
Compounding periods (n ): 4 (quarterly).
Use the formula for effective annual yield (A):
A = (1 + r/n)ⁿ - 1
Plug the numbers into the formula:
A = (1 + 0.05/4)⁴ - 1
Calculate inside the parentheses first:
1 + 0.05/4 = 1.0125
Raise the result to the power of 4:
(1.0125)⁴ ≈ 1.05095
Subtract 1 to get the effective annual yield:
1.05095 - 1 ≈ 0.05095 or 5.095%
Therefore, the effective annual yield is approximately 5.1%, rounded to the nearest tenth of %.
Complete question:
A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is compounded quarterly. The effective annual yield is %. (Round to the nearest tenth as needed.)
Find the diameter! *
Surface Area = 28.26 ft
diameter =
O ZA
O 3ft
O 4H
5ft
Answers
Known :
Sa = 28.26 ft
Asked :
d = ...?
Answer :
Sa = 4πr²
28.26 = 4 × 3.14 × r²
28.26 = 12.56 r²
r² = 28.26 ÷ 12.56
r² = 2.25
r = √2.25
r = 1.5 ft
diameter = 2 × radius = 2 × 1.5 = 3 ft
So, the diameter is 3 ft (2nd choice)
Hope it helpful and useful :)
Step-by-step explanation:
SA = 4 [tex]\pi[/tex]
28.26 = 4 × 22/7 × r²
r³ = 28.26 × 7/88
r² = 2.25 ft²
r = 1.5 ft
Diameter = 2 × r = 3 ft
can anyone help? I’m confused:(
Answers
Answer:
The answer is -1.
Step-by-step explanation:
( 1 + 3 ) - 6 / 2
(4) - 6 / 2
-2 / 2
-1
2. Use the distance formula to find the lengths of the sides of
the second triangle, Astu.
V-2 - (-8»? + (-7 - (-3)? = V6? + (-4)2
= 36 + 16 = 52 = 4(13)
4(13) = 2V13
The length of ST is 5. What is the length of TU?
53
85
45
Answers
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
just did it on Edge
a 15 inch long windshield wiper blade swipes in arc of 120°. How many square inches of a windshield’s surface area does the blade cover in one swipe
Answers
The blade covers an area of 235.714 square inches in one swipe.
In this question, we are to calculate the area that is covered by blade cover of the windshield wiper blade in 1 swipe.
To calculate this, we shall be using the formula for the area of the sector. The sector in this case subtends an angle of 120 degrees at the centre.
Mathematically, the area covered by the blade in one swipe is
A = θ/360 * pi * r^2
where θ = 120 degrees and r = 15 inch
A = 120/360 * 22/7 * 15^2
= 1/3 * 22/7 * 225 = 22 * 75/7 = 235.714 square inches
I have a picture attached I am offering 35 points I need these questions done ASAP
Answers
Answer:its not showing me the picture
Step-by-step explanation:
Answer:
1.32
4. 35
5. 400
7. 225
8. 260
10. 77
11. 72
Step-by-step explanation:
NEED RNN!!!!!
Ten people at two local restaurants were randomly
surveyed and asked to rate their experience, with "1"
representing very poor and "10" representing very
good. The data is shown in the dot plots.
Find the mean for each set of data.
Blue Terrace:
Paradiso Grill:
Answers
Answer: 6.1 and 6.3
Step-by-step explanation: just did it
PLEASE HELP!!! HURRY PLEASE!!!
consider the. system of equations:
y=-2x+4
y=-1/3x-1
the solution is (3, -2)
verify the solution. which true statement appesrs in your check?
a.4=4
b.-2=-2
c.-1=-1
d.-3=-3
Answers
Answer:-2=-2 (b)
Step-by-step explanation:
I just took that lesson
Answer:
-2=-2
Step-by-step explanation:
Charles wants to find out if the students in foreign language classes spend more time in class speaking in English or in the for
language they are studying. Charles first gets class lists of all students taking foreign language classes. He then chooses 10
students from each different language class to survey. Which best explains why the sample he chose may not be a
representative sample?
The sample size is not large enough to renresent the nonulation
Answers
Answer:
The way the sample was chosen may overrepresent or underrepresent students taking certain language classes.
Step-by-step explanation:
Answer options:
The sample size is not large enough to represent the population.
No. Sample size is quite small per language.The sample was not chosen at random.
No. There is no evidence if samples are not random.The way the sample was chosen may overrepresent or underrepresent students taking certain language classes.
Yes. Some of the classes my have large, some may have small population. Therefore taking 10 samples from each language is not right proportion and proper representation.The way the sample was chosen does not sample students from each different language class.
No. Each language class is considered.Answer:
C
Step-by-step explanation:
The way the sample was chosen may overrepresent or underrepresent students taking certain language classes.
Standard for
ola (y + 3)2 = -12(x - 2), iden
1.
D
n111
Answers
Answer:
See below
Step-by-step explanation:
Your question is a bit unclear, so I'm going to assume you want the value of y or x:
(y+3)^2=-12(x-2)
-(y+3)^2/12=x-2
-(y+3)^2/12+2=x
(y+3)^2=-12(x-2)
y+3=sqrt(-12x+24)
y=sqrt(-12x+24)-3
I need help please i don’t understand
Answers
Answer:
C
Step-by-step explanation:
If the volume of the pyramid shown is 108 inches cubed, what is the area of its base? A pyramid with a height of 8 inches. 4 inches squared 12 inches squared 24 inches squared 36 inches squared
Answers
Answer:
36in²
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a square based pyramid.
Step one
The formula for the volume of a square based pyramid is
V=a²h/3
Where a = side of base
h= height
Given data
Volume = 108in³
Height h= 8 in
We can solve for the base a by substituting our data
108= a²* 8/3
a²= (108*3)/8
a²= 40.5
a= √40.5
a= 6.36in
To the nearest whole number
a= 6in
The area of the square based = 6*6
= 36in²
Answer:
D. 36
Step-by-step explanation: stay calm and smile
Marking Brainliest! Please :))
Answers
Answer:
23/137
Step-by-step explanation:
im guessing i hope u get it right.
The solutions of a quadratic function are its y-intercepts. Ture or false
Answers
Answer:
True
Step-by-step explanation:
Answer:
i think the answer is true
Step-by-step explanation:
What is the slope of the line?
Answers
Answer:
slope = 1
Step-by-step explanation:
(3,0) ; (0, -3)
[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-3-0}{0-3}\\\\=\frac{-3}{-3}\\\\=1[/tex]