A cylinder has a height of 20cm.
The circumference of the cylinder is 8π cm.
Calculate the volume of the cylinder in terms of π.
From your data:
2πr = 8π
r = 4
So the radius is 4 cm
volume of cylinder = πr^2 h
you know both r and h, so plug in and evaluate
Oh, boy! It's time for a math-filled circus act! To calculate the volume of this cylinder, we need to know the radius. Luckily, we can figure it out from the circumference.
The formula for circumference is C = 2πr, where C is the circumference and r is the radius. We know that the circumference is 8π cm, so we can set up an equation:
8π = 2πr
Now, we can solve for the radius:
r = (8π)/(2π)
r = 4 cm
Now, let's get down to some volume fun! 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. Plug in the values:
V = π(4^2)(20)
V = 320π cm³
So, the volume of the cylinder, in terms of π, is 320π cm³. Thank you for joining the math circus!
To calculate the volume of a cylinder, you can use the formula 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 circumference of the cylinder is 8π cm, we can find the radius by using the formula C = 2πr, where C is the circumference.
Using the given information, we have:
8π cm = 2πr
Divide both sides by 2π to solve for r:
4 = r
Now that we know the radius is 4 cm and the height is 20 cm, we can calculate the volume of the cylinder:
V = π(4^2)(20)
V = π(16)(20)
V = 320π cm^3
Therefore, the volume of the cylinder in terms of π is 320π cm^3.
To calculate the volume of a cylinder, you need to know the height and the radius of the base. In this case, we are given the height of the cylinder, which is 20 cm.
To find the radius of the base, we can use the formula for the circumference of a cylinder, which is 2πr, where r is the radius. In this case, the circumference is given as 8π cm, so we can set up the equation:
2πr = 8π
To solve for the radius, divide both sides of the equation by 2π:
r = 8π / (2π)
Simplifying the expression:
r = 4
Now that we have the height and the radius of the cylinder, we can use the formula for the volume of a cylinder, which is V = πr^2h, where V is the volume. Plugging in the values:
V = π(4^2)(20)
Simplifying:
V = π(16)(20)
V = 320π
Therefore, the volume of the cylinder in terms of π is 320π cubic centimeters.