Question

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)

Answer 1

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.