Writing Find the volume of a cylinder with radius 10 m and height 3 m. Use pencil and paper. How does the volume change when the height is tripled? When the radius is tripled?3
(Type an exact answer in terms of pie)
To find the volume of a cylinder, we can use the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given:
Radius, r = 10 m
Height, h = 3 m
Substituting the given values into the formula, we get:
V = π(10^2)(3)
V = π(100)(3)
V = 300π
So the volume of the cylinder is 300π cubic meters.
When the height is tripled, the new height, h' = 3 * 3 = 9 m.
Substituting the new height into the formula, we get:
V' = π(10^2)(9)
V' = π(100)(9)
V' = 900π
So when the height is tripled, the new volume is 900π cubic meters.
When the radius is tripled, the new radius, r' = 10 * 3 = 30 m.
Substituting the new radius into the formula, we get:
V' = π(30^2)(3)
V' = π(900)(3)
V' = 2700π
So when the radius is tripled, the new volume is 2700π cubic meters.