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
Hello Brent, I have a question isn't the volume of a cylinder with r = 2 and height = 3 = \(pi* r^2 * h\) and in this case \(pi * 2^2 * 3\) = \(12pi\) and hence the volume of the cube should be 12pi or closest value less than that and from the option choice E?