Question

A cylinder has a diameter of 18 inches and a volume of 405 /2 π cubic inches. What is the height, in inches, of the cylinder? Enter the height in decimal form rounded to the nearest tenth.

Answer 1

The answer is 2.5 inches.

The volume (V) of the cylinder with radius r and height h is: V = π r² h

Let's express it in the terms of h: h = V / (π * r²)

We know that radius is half of the diameter:
r = 18/2 = 9 in
V = 405/2 π in³ = 202.5π in³

h = V / (π * r²)
h = 202.5π / (π * 9²)
h = 202.5π / 81π
h = 2.5 in