A cylinder has a height of 12cm.
The circumference of the cylinder is 20π cm.
Calculate the volume of the cylinder in terms of π
Dont talk about my butler like that
Well, if the circumference of the cylinder is 20π cm, then the formula for the circumference of a cylinder (C) is 2πr, where r is the radius. So, we can set up the equation:
2πr = 20π
To determine the value of r, we can divide both sides of the equation by 2π:
r = 10
Now, we can calculate the volume (V) of the cylinder using the formula V = πr^2h, where h is the height:
V = π(10)^2(12)
V = 1200π cm³
So, the volume of the cylinder in terms of π is 1200π cm³. And no, I didn't mean to say "pied"! It's 1200π cm³, not 1200 pumpkin pies!
To calculate the volume of a cylinder, you need to 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.
In this case, we are given the height h = 12 cm and the circumference of the cylinder 20π cm.
The circumference of a cylinder can be found using the formula C = 2πr, where C is the circumference and r is the radius.
We are given that the circumference is 20π cm, so we have 20π = 2πr.
From this equation, we can solve for the radius r:
20π = 2πr
Divide both sides by 2π:
10 = r
Now we have the radius r = 10 cm and the height h = 12 cm.
Using the formula for the volume of a cylinder, we can substitute the values:
V = πr^2h
V = π(10 cm)^2(12 cm)
V = 120π cm^3
Therefore, the volume of the cylinder is 120π cm^3.
the radius is 10 cm (think about it)
volume = π * radius^2 * height