The volume of a cylinder varies jointly with the square of its radius and with its height: V=kr^2h
Cylinder A has a volume of 251.2 cubic inches and has a radius of 4 inches and a height of 5 inches. What is the volume of cylinder B, which has a radius of 3 inches and a height of 9 inches?
To find the volume of cylinder B, we can use the equation V = kr^2h and solve for k using the given information about cylinder A.
The volume of cylinder A is 251.2 cubic inches. The radius of cylinder A is 4 inches and the height is 5 inches.
251.2 = k * 4^2 * 5
251.2 = k * 16 * 5
251.2 = 80k
k = 251.2 / 80
k ≈ 3.14
Now that we have the value of k, we can find the volume of cylinder B.
The radius of cylinder B is 3 inches and the height is 9 inches.
V = 3.14 * 3^2 * 9
V = 3.14 * 9 * 9
V ≈ 254.34 cubic inches
Therefore, the volume of cylinder B is approximately 254.34 cubic inches.