Question

A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters.

A cylinder is shown. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters. The diameter of the larger cylinder is 20 millimeters, and the the radius of the smaller cylinder is 6 millimeters.

Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.

21π(10)2 – 21π(6)2
π(20)2(21) – π(6)2
2,100π – 756π
7,644π
1,344

Answer 1

Select the first and third options.

Reason: Volume = π(10^2)(21) − π(6^2)(21) = 21π(10)^2 − 21π(6)^2 = 2,100π − 756π = 1,344π.