A cylinder has a volume of 132 pi cubic feet and height of 4 feet. What is the area of the base?
Pi square feet
We can use the formula for the volume of a cylinder, V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. Given that the volume, V, is 132π cubic feet and the height, h, is 4 feet, we can solve for the radius, r, as follows:
132π = πr^2(4)
132 = 4r^2
r^2 = 33
r = √33
The area of the base, A, is given by the formula A = πr^2, where A is the area and r is the radius. Substituting the value of √33 for r, we get:
A = π(√33)^2
A = π * 33
A = 33π
Therefore, the area of the base of the cylinder is 33π square feet, or approximately 103.67 square feet.
A sphere has a diameter of 14 ft. Which equation finds the volume of the sphere?
V = four-thirds (7) cubed
V = four-thirds pi (7) cubed
V = four-thirds (14) cubed
V = four-thirds pi (14) cubed
The correct equation to find the volume of the sphere is:
V = four-thirds pi (7) cubed
In this equation, "V" represents the volume of the sphere, and the radius of the sphere is half of the diameter, which is 7 ft in this case.
A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches. Which equation can be used to find the volume of the container?
V = one-third pi (2) squared (9)
V = one-third pi (4) squared (9)
V = one-third pi (4) (9) squared
V = one-third pi (2) (9) squared
The correct equation to find the volume of the popcorn container is:
V = one-third pi (2) squared (9)
In this equation, "V" represents the volume of the container. We need to use the formula for the volume of a cone, which is V = one-third pi r^2 h, where "r" is the radius of the circular opening and "h" is the height of the cone.
Given that the diameter of the circular opening is 4 inches, the radius is half of that, which is 2 inches. The height of the cone is given as 9 inches. Plugging these values into the volume formula, we get:
V = one-third pi (2)^2 (9)
Marina sells candles that are in the shape of cones. She makes a yellow candle that has a diameter of 4 inches and a height of 11 inches. She sells each candle at a price of $0.35 per cubic inch of wax. Which statements about the yellow candle are true? Check all that apply. Use 3.14 for Pi.
The volume of the yellow candle is about 46.05 inches cubed.
The volume of the yellow candle is about 184.21 inches cubed.
The radius of the yellow candle is 2 in.
The radius of the yellow candle is 8 in.
The base area of the yellow candle is about 6.28 inches squared.
The base area of the yellow candle is about 12.56 inches squared.
The price of one yellow candle is about $64.47.
The price of one yellow candle is about $16.12.
To determine which statements about the yellow candle are true, we can calculate its volume, radius, base area, and price.
First, let's calculate the volume of the yellow candle using the formula for the volume of a cone:
V = 1/3 * pi * r^2 * h
Given that the diameter is 4 inches, the radius is half of that, which is 2 inches, and the height is 11 inches.
V = 1/3 * 3.14 * 2^2 * 11
V ≈ 46.05 inches cubed
So, the statement "The volume of the yellow candle is about 46.05 inches cubed" is true.
Next, let's calculate the radius of the yellow candle. We already know that the radius is 2 inches.
So, the statement "The radius of the yellow candle is 2 in" is true, and the statement "The radius of the yellow candle is 8 in" is false.
Now, let's calculate the base area of the yellow candle using the formula for the area of a circle:
A = pi * r^2
Given that the radius is 2 inches:
A = 3.14 * 2^2
A ≈ 12.56 inches squared
So, the statement "The base area of the yellow candle is about 12.56 inches squared" is true.
Finally, let's calculate the price of one yellow candle. We multiply the volume of the candle by the price per cubic inch:
Price = V * $0.35
Price ≈ 46.05 * 0.35
Price ≈ $16.12
So, the statement "The price of one yellow candle is about $16.12" is true.
In conclusion, the following statements are true about the yellow candle:
- The volume of the yellow candle is about 46.05 inches cubed.
- The radius of the yellow candle is 2 in.
- The base area of the yellow candle is about 12.56 inches squared.
- The price of one yellow candle is about $16.12.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed.
A sphere with height h and radius r. A cylinder with height h and radius r.
What is the volume of the sphere?
6 meters cubed
7 meters cubed
14 meters cubed
28 meters cubed
We are given that the volume of the cylinder is 21 meters cubed. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the sphere and cylinder have the same radius and height, we can call the common radius and height "r" and "h" respectively.
Given that the volume of the cylinder is 21 meters cubed, we have:
21 = πr^2h
To find the volume of the sphere, we can use the formula for the volume of a sphere, which is V = (4/3)πr^3.
Since the sphere and cylinder have the same radius, we can substitute r with r in the equation:
V = (4/3)πr^3
We know that the volume of the cylinder is 21 meters cubed, so we can equate the two equations:
21 = (4/3)πr^3
Now we can solve for V, the volume of the sphere:
V = (4/3)πr^3
V = (4/3)(21/π)
V = 28
Therefore, the volume of the sphere is 28 meters cubed.
To find the area of the base of a cylinder, we need to use the formula for the volume of a cylinder. The volume of a cylinder is given by the formula:
V = πr^2h
where V is the volume, π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.
In this case, we are given the volume V as 132π cubic feet and the height h as 4 feet. We want to find the area of the base, so we need to find the radius r first.
To find the radius, we need to rearrange the formula for the volume of a cylinder:
V = πr^2h
Dividing both sides by πh, we get:
r^2 = V / (πh)
Substituting the given values, we have:
r^2 = (132π) / (π * 4)
= 33
Now, we can take the square root of both sides to find the value of r:
r = √33
Therefore, the radius of the base of the cylinder is √33 feet.
To find the area of the base, we can use the formula for the area of a circle:
A = πr^2
Substituting the value of r, we have:
A = π(√33)^2
= π * 33
= 33π
So, the area of the base of the cylinder is 33π square feet.