The volume of a cone with a height of 6 cm is 8 pi cubic centimeters. Which expression can be used to find r, the radius of the base of the cone?
6 = one-third pi (r squared) (8 pi)
8 pi = one-third pi (r) (6 squared)
6 = one-third (pi r)(8 pi)
8 pi = one-third pi (r squared) (6)
The volume of a cone with a height of 6 cm is 8 pi cubic centimeters. Which expression can be used to find r, the radius of the base of the cone?
6 = one-third pi (r squared) (8 pi)
8 pi = one-third pi (r) (6 squared)
6 = one-third (pi r)(8 pi)
8 pi = one-third pi (r squared) (6)
The correct expression to find the radius, r, of the base of the cone is:
8π = (1/3)πr^2(6)
Simplifying further:
8π = 2πr^2
Now we can divide both sides of the equation by 2π to solve for r:
r^2 = (8π) / (2π)
r^2 = 4
Taking the square root of both sides:
r = ±2
Since radius cannot be negative, the correct value for r is:
r = 2 cm
What is the height of the cone below?
A cone with base of 18 centimeters squared and volume of 90 centimeters cubed.
5 cm
6 cm
15 cm
30 cm
To find the height of the cone, we need to use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given that the base of the cone has an area of 18 cm^2 and the volume is 90 cm^3, we can write the equation as:
90 = (1/3) * π * 18 * h
Simplifying further:
90 = (6/3) * π * h
90 = 2πh
To solve for h, we can divide both sides of the equation by 2π:
h = 90 / (2π)
Now, let's calculate the value of h:
h = 90 / (2 * 3.14159)
h ≈ 14.33 cm
Therefore, the height of the cone is approximately 14.33 cm.
try again ur incorrect
helo
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awnser the previous question
Apologies for the mistake in my previous response. Let's re-evaluate the question.
Given that the base of the cone has an area of 18 cm^2 and the volume is 90 cm^3, we can use the formula for the volume of a cone to find the height, h.
The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
We are given that the base area is 18 cm^2. The formula for the area of a circle is A = π * r^2. So, we can determine the radius, r, by solving the equation:
18 = π * r^2
Simplifying further:
r^2 = 18 / π
Taking the square root of both sides:
r ≈ √(18 / π)
Now, we can substitute the value of r into the volume equation:
90 = (1/3) * π * (√(18 / π))^2 * h
Simplifying further:
90 = (1/3) * π * (18 / π) * h
90 = 6 * h
Dividing both sides of the equation by 6:
h = 90 / 6
h = 15 cm
Therefore, the height of the cone is 15 cm.
Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Which statements about the green candle are true? Check all that apply. Use 3.14 for Pi.
The volume of the green candle is about 23.55 inches cubed.
The volume of the green candle is about 58.88 inches cubed.
The diameter of the green candle is 5 in.
The diameter of the green candle is 1.25 in.
The base area of the green candle is about 19.63 inches squared.
The base area of the green candle is about 7.85 inches squared.
The price of one green candle is about $5.89.
The price of one green candle is about $14.72.
To determine which statements about the green candle are true, let's calculate and compare the relevant values.
Given:
Radius (r) = 2.5 inches
Height (h) = 9 inches
Pi (π) = 3.14
1. The volume of the green candle:
The formula for the volume of a cone is V = (1/3)πr^2h.
Substituting the given values:
V = (1/3) * 3.14 * (2.5^2) * 9
V ≈ 58.88 cubic inches
2. The diameter of the green candle:
The diameter of a circle is twice the radius.
diameter = 2 * radius = 2 * 2.5 = 5 inches
3. The base area of the green candle:
The formula for the area of a circle is A = πr^2.
Substituting the given values:
A = 3.14 * (2.5^2)
A ≈ 19.63 square inches
4. The price of one green candle:
Using the given selling rate of $0.25 per cubic inch of wax, we can calculate the price.
Price = volume * rate = 58.88 * 0.25
Price ≈ $14.72
Based on these calculations, the statements that are true are:
- The volume of the green candle is about 58.88 inches cubed.
- The diameter of the green candle is 5 inches.
- The base area of the green candle is about 19.63 inches squared.
- The price of one green candle is about $14.72.
What is the area of the base of the cone below? Round the answer to the nearest tenth if necessary.
A cone with height 8 inches and volume 52 inches cubed.
14.7 inches squared
17.3 inches squared
18.5 inches squared
19.5 inches squared
To find the area of the base of the cone, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given that the height of the cone is 8 inches and the volume is 52 inches cubed, we can write the equation as:
52 = (1/3) * π * r^2 * 8
Rearranging the equation:
r^2 = (52 * 3) / (π * 8)
Simplifying further:
r^2 ≈ 6.53
Taking the square root of both sides:
r ≈ 2.56
Now, we can calculate the area of the base of the cone using the formula for the area of a circle:
A = π * r^2
Substituting the value of r:
A ≈ 3.14 * (2.56^2)
A ≈ 3.14 * 6.55
A ≈ 20.53 inches squared
Therefore, the area of the base of the cone is approximately 20.53 inches squared.
try again
Apologies for the mistake in my previous response. Let's re-evaluate the question.
Given that the height of the cone is 8 inches and the volume is 52 inches cubed, we can find the radius using the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Substituting the given values:
52 = (1/3) * π * r^2 * 8
Simplifying further:
52 = (8/3) * π * r^2
To isolate the r^2 term, we can divide both sides of the equation by (8/3) * π:
r^2 = 52 / ((8/3) * π)
r^2 ≈ 2.624
Taking the square root of both sides:
r ≈ √2.624
r ≈ 1.62 inches
Now, we can calculate the area of the base using the formula for the area of a circle:
A = π * r^2
Substituting the value of r:
A ≈ π * (1.62^2)
A ≈ π * 2.624
A ≈ 8.24 inches squared (rounded to the nearest tenth)
Therefore, the area of the base of the cone is approximately 8.2 inches squared.
What is the area of the base of the cone below? Round the answer to the nearest tenth if necessary.
A cone with height 8 inches and volume 52 inches cubed.
14.7 inches squared
17.3 inches squared
18.5 inches squared
19.5 inches squared
try again
To find the area of the base of the cone, we need to first find the radius of the cone.
Given:
Height (h) = 8 inches
Volume (V) = 52 inches cubed
We can use the formula for the volume of a cone to find the radius (r):
V = (1/3) * π * r^2 * h
Plugging in the given values:
52 = (1/3) * π * r^2 * 8
Simplifying:
r^2 = (52 * 3) / (π * 8)
r^2 ≈ 6.53
Taking the square root of both sides:
r ≈ 2.56 inches
Now that we have the radius, we can find the area of the base of the cone using the formula for the area of a circle:
A = π * r^2
Plugging in the value of r:
A ≈ π * (2.56)^2
A ≈ π * 6.57
A ≈ 20.62 inches squared
Now, rounding to the nearest tenth, the area of the base of the cone is approximately 20.6 inches squared.
None of the provided answer options, 14.7, 17.3, 18.5, or 19.5 inches squared, are correct. The correct answer is approximately 20.6 inches squared.
An icicle is in the shape of an inverted cone with a diameter of 14 mm and a height of 60 mm. How much frozen water is in the icicle? Use 3.14 for Pi. Round the answer to the nearest tenth.
188.4 millimeters cubed
980.0 millimeters cubed
3,077.2 millimeters cubed
9,231.6 millimeters cubed
To find the volume of the icicle, we need to calculate the volume of the inverted cone.
Given:
Diameter of the icicle (d) = 14 mm
Radius of the icicle (r) = d/2 = 14/2 = 7 mm
Height of the icicle (h) = 60 mm
Pi (π) = 3.14
The formula for the volume of a cone is V = (1/3) * π * r^2 * h.
Plugging in the given values, we have:
V = (1/3) * 3.14 * (7^2) * 60
V = (1/3) * 3.14 * 49 * 60
V ≈ 3.14 * 49 * 20
V ≈ 3077.2 mm^3
Rounded to the nearest tenth, the volume of frozen water in the icicle is approximately 3077.2 mm^3.
Therefore, the correct answer is: 3077.2 millimeters cubed.
The volume of a cone with a radius of 7 cm is 147 pi cubic centimeters. Which expression can be used to find h, the height of the cone?
147 pi = one-third (7) (h) squared
147 pi = one-third pi (7 squared) (h)
147 pi = one-third pi h
147 pi = one-third pi (7) (h)
The correct expression to find the height, h, of the cone is:
147π = (1/3)π * (7^2) * h
Simplifying further:
147π = (49/3)π * h
Now we can divide both sides of the equation by (49/3)π to solve for h:
h = 147π / (49/3)π
h = (147 / (49/3)) * (π/π)
h = (147 / (49/3)) * 3
h = 147 / 49 * 3
h = 3 * 3
h = 9 cm
Therefore, the correct expression to find the height, h, of the cone is:
147π = (1/3)π * (7^2) * h