a cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. a cylindrical hole…

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

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

Answer

Explanation:

Step1: Recall volume - formula for cylinder

The volume formula for a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Find outer - cylinder volume

The outer - cylinder has a diameter of 20 mm, so the radius $r_{1}=\frac{20}{2}=10$ mm and height $h = 21$ mm. Its volume $V_{1}=\pi r_{1}^{2}h=21\pi(10)^{2}$.

Step3: Find inner - cylinder volume

The inner - cylinder (the hole) has a radius $r_{2} = 6$ mm and height $h = 21$ mm. Its volume $V_{2}=21\pi(6)^{2}$.

Step4: Calculate volume of metal

The volume of metal needed is $V = V_{1}-V_{2}=21\pi(10)^{2}-21\pi(6)^{2}$. Expanding $21\pi(10)^{2}=21\times100\pi = 2100\pi$ and $21\pi(6)^{2}=21\times36\pi=756\pi$, so $V = 2100\pi - 756\pi$.

Answer:

  1. $21\pi(10)^{2}-21\pi(6)^{2}$
  2. $2100\pi - 756\pi$