Question

1. complete this table for different cylinders.

diameter (units)	radius (units)	base area (sq. units)	height (units)	cylinder volume (cu. units)
6			5
		$36\pi \approx 113.04$		$144\pi \approx 452.16$

Explanation:

Step1: Find diameter and base area for radius = 5

• Diameter \(d = 2r\). Given \(r = 5\), then \(d=2\times5 = 10\).
• Base area of a cylinder (area of a circle) \(A=\pi r^{2}\). Substitute \(r = 5\), \(A=\pi\times5^{2}=25\pi\approx 25\times 3.14=78.5\).
• Volume of a cylinder \(V = A\times h\). Substitute \(A = 25\pi\) and \(h = 7\), \(V=25\pi\times7=175\pi\approx175\times3.14 = 549.5\).

Step2: Find radius and base area for diameter = 6

• Radius \(r=\frac{d}{2}\). Given \(d = 6\), then \(r=\frac{6}{2}=3\).
• Base area \(A=\pi r^{2}\). Substitute \(r = 3\), \(A=\pi\times3^{2}=9\pi\approx9\times3.14 = 28.26\).
• Volume \(V=A\times h\). Substitute \(A = 9\pi\) and \(h = 5\), \(V=9\pi\times5 = 45\pi\approx45\times3.14=141.3\).

Step3: Find radius and height for base area \(A = 36\pi\) and volume \(V=144\pi\)

• Since \(A=\pi r^{2}=36\pi\), then \(r^{2}=36\), \(r = 6\).
• Since \(V=A\times h\), and \(V = 144\pi\), \(A=36\pi\), then \(h=\frac{V}{A}=\frac{144\pi}{36\pi}=4\).

Answer:

Diameter (units)	Radius (units)	Base Area (sq. units)	Height (units)	Cylinder Volume (cu. units)
\(6\)	\(3\)	\(9\pi\approx28.26\)	\(5\)	\(45\pi\approx141.3\)
\(12\)	\(6\)	\(36\pi\approx113.04\)	\(4\)	\(144\pi\approx452.16\)