A cylinder has a volume of \(180\pi\) cubic inches and the radius of its circular base is 6 inches. What is the length

Gmat_mission wrote: ↑

Sun Jun 14, 2020 2:32 pm

A cylinder has a volume of \(180\pi\) cubic inches and the radius of its circular base is 6 inches. What is the length of the longest line segment that can be drawn from one point on the cylinder to another?

A. \(\dfrac{30}{\pi}\)
B. \(12\)
C. \(13\)
D. \(5\pi\)
E. \(6\pi\)

[spoiler]OA=C[/spoiler]

Solution:

The longest line segment that can be drawn from one point on the cylinder to another is √[h^2 + (2r)^2], where h is the height of the cylinder and r is the radius of its base (notice that 2r is actually the diameter of the base). (Note that this is simply the Pythagorean theorem, where the two sides of the triangle are the height of the cylinder and the diameter of the cylinder.)

In this problem, we are given the radius of the cylinder but not its height. Therefore, we need to determine the height of the cylinder. Recall that the volume of a cylinder is π * r^2 * h. Therefore, we have:

π * 6^2 * h = 180π

36πh = 180π

h = 5

So, the longest line segment is √[5^2 + (2 * 6)^2] = √(25 + 144) = √169 = 13 inches long.

Answer: C