Writing Find the volume of a cylinder with radius 6 m and height 4 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 represents the volume, r represents the radius, and h represents the height.
Given that the radius is 6 m and the height is 4 m, we can substitute these values into the formula:
V = π(6^2)(4)
V = π(36)(4)
V = π(144)
V = 144π
The volume of the cylinder is 144π m^3.
When the height is tripled, the new height becomes 4 x 3 = 12 m.
Plugging this new height into the formula, we get:
V = π(6^2)(12)
V = π(36)(12)
V = π(432)
V = 432π
The new volume with tripled height is 432π m^3.
When the radius is tripled, the new radius becomes 6 x 3 = 18 m.
Plugging this new radius into the formula, we get:
V = π(18^2)(4)
V = π(324)(4)
V = π(1296)
V = 1296π
The new volume with tripled radius is 1296π m^3.