BTGmoderatorLU wrote: ↑

Wed Mar 11, 2020 6:11 pm

Source: Official Guide

A container in the shape of a right circular cylinder is \(1/2\) full of water. If the volume of water in the container is \(36\) cubic inches and the height of the container is \(9\) inches, what is the diameter of the base of the cylinder, in inches?

A. \(\dfrac{16}{9\pi}\)

B. \(\dfrac{4}{\pi}\)

C. \(\dfrac{12}{\pi}\)

D. \(\sqrt{\dfrac{2}{\pi}}\)

E. \(4\sqrt{\dfrac{2}{\pi}}\)

The OA is E

From the given information, we know that 1/2 the volume of the cylinder = 36 cc;

Thus, the volume of the cylinder = 72 cc

We also know that the volume of the cylinder is given by πr^2h; we are also given that h = 9 inches

Thus, V = πr^2h = π*r^2*9 => r = 2√(2/π)

Thus, diameter = 2r = 2*2√(2/π) = 4√(2/π) inches

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Wed Mar 11, 2020 6:11 pm

Source: Official Guide

A container in the shape of a right circular cylinder is \(1/2\) full of water. If the volume of water in the container is \(36\) cubic inches and the height of the container is \(9\) inches, what is the diameter of the base of the cylinder, in inches?

A. \(\dfrac{16}{9\pi}\)

B. \(\dfrac{4}{\pi}\)

C. \(\dfrac{12}{\pi}\)

D. \(\sqrt{\dfrac{2}{\pi}}\)

E. \(4\sqrt{\dfrac{2}{\pi}}\)

The OA is E

Recall that the volume of a cylinder is:

volume = π(radius)^2(height)

Since half of the capacity of the cylinder is 36, the full capacity of the cylinder is 72; thus:

72 = πr^2(9)

8/π = r^2

√(8/π) = r

√8/√π = r

(2√2)/√π = r

2√(2/π) = r

The diameter is twice the radius. Thus, the diameter is 2 x 2√(2/π) = 4√(2/π).

Answer: E