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 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches. What is the volume of cylinder B, which has a radius of 4 inches and a height of 5 inches?
A. 188.4 cubic inches
B. 251.2 cubic inches
C. 62.8 cubic inches
D. 3.14 cubic inches
First, we can use the given information about cylinder A to find the value of k in the equation. Plugging in V = 254.34, r = 3, and h = 9, we get:
254.34 = k(3^2)(9)
254.34 = 81k
k = 254.34/81
k = 3.14
Now we can use this value of k to find the volume of cylinder B. Plugging in V = ?, r = 4, and h = 5, we get:
V = (3.14)(4^2)(5)
V = 251.2
Therefore, the volume of cylinder B is 251.2 cubic inches, which is answer choice B.