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 the volume of the large cylinder

The formula for the volume of a cylinder is \(V = \pi r^{2}h\). The diameter of the large cylinder is \(d = 20\) mm, so the radius \(r=\frac{d}{2}=10\) mm and height \(h = 21\) mm. The volume of the large cylinder \(V_{1}=\pi\times(10)^{2}\times21 = 21\pi(10)^{2}\).

Step2: Calculate the volume of the small cylinder (hole)

The radius of the small cylinder \(r = 6\) mm and height \(h = 21\) mm. The volume of the small cylinder \(V_{2}=\pi\times(6)^{2}\times21=21\pi(6)^{2}\).

Step3: Find the volume of the metal (difference of volumes)

The volume of the metal \(V = V_{1}-V_{2}=21\pi(10)^{2}-21\pi(6)^{2}\).
Simplify \(21\pi(10)^{2}-21\pi(6)^{2}\):

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Also, \(21\pi(10)^{2}=21\times100\pi = 2100\pi\) and \(21\pi(6)^{2}=21\times36\pi=756\pi\), so \(V=2100\pi - 756\pi\)

Answer:

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