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?
To find the volume of a cylinder, we can use the formula V = πr²h, 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 to find the volume.
V = π(6²)(4)
V = π(36)(4)
V = 144π
V ≈ 452.39 cubic meters
To determine how the volume changes when the height is tripled, we'll consider the new height as h'.
The new volume V' = πr²h'.
Given that the new height is tripled, h' = 3h = 3(4) = 12 m.
Substituting the new height into the formula using the original radius, we get:
V' = π(6²)(12)
V' = π(36)(12)
V' = 432π
V' ≈ 1357.17 cubic meters
Therefore, the volume increases from approximately 452.39 cubic meters to 1357.17 cubic meters when the height is tripled.
To determine how the volume changes when the radius is tripled, we'll consider the new radius as r''.
The new volume V'' = π(r'')²h.
Given that the new radius is tripled, r'' = 3r = 3(6) = 18 m.
Substituting the new radius into the formula using the original height, we get:
V'' = π(18²)(4)
V'' = π(324)(4)
V'' = 1296π
V'' ≈ 4071.5 cubic meters
Therefore, the volume increases from approximately 452.39 cubic meters to 4071.5 cubic meters when the radius is tripled.