GreenlightTestPrep 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

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

Since the radius of the cylinder is 2, we know that the

DIAMETER = 4Since 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

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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