What is the volume of the largest cube that can

Brent@GMATPrepNow wrote:What is the volume of the largest cube that can fit inside a cylinder with radius 2 and height 3?
A) 9
B) 8√2
C) 16
D) 16√2
E) 27

Answer: D
Difficulty level: 650 – 700
Source: www.gmatprepnow.com

Let's first inscribe the largest possible square inside the circle



Since the radius of the cylinder is 2, we know that the DIAMETER = 4


Since we have a RIGHT TRIANGLE, we can apply the Pythagorean Theorem to get: x² + x² = 4²
Simplify: 2x² = 16
So, x² = 8, which means x = √8 = 2√2

ASIDE: On test day, you should know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, we get: x = 2√2 ≈ 2(1.4) ≈ 2.8



At this point, we should recognize that, since the height of the cylinder is 3...

...then the LARGEST CUBE will have dimensions 2√2 by 2√2 by 2√2

Volume = (2√2)(2√2)(2√2)
= 8√8
= 8(2√2)
= 16√2

Answer: D

Cheers,
Brent