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. 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

Explanation:

Step1: Calculate outer - cylinder volume

The formula for the volume of a cylinder is $V = \pi r^{2}h$. The outer - radius of the pipe $r_{1}=\frac{20}{2}=10$ mm and height $h = 21$ mm. So the volume of the outer - cylinder $V_{1}=\pi r_{1}^{2}h=21\pi(10)^{2}$.

Step2: Calculate inner - cylinder volume

The inner - radius of the pipe $r_{2} = 6$ mm and height $h = 21$ mm. So the volume of the inner - cylinder $V_{2}=\pi r_{2}^{2}h=21\pi(6)^{2}$.

Step3: Calculate volume of metal

The volume of metal needed to make the pipe is the difference between the volume of the outer - cylinder and the volume of the inner - cylinder, $V = V_{1}-V_{2}=21\pi(10)^{2}-21\pi(6)^{2}$.
Simplify $21\pi(10)^{2}-21\pi(6)^{2}=21\pi(100 - 36)=21\pi\times64 = 1344\pi=2100\pi-756\pi$.

Answer:

$21\pi(10)^{2}-21\pi(6)^{2}$, $2100\pi - 756\pi$