Question

a cylinder with a base diameter of 6 in and a height of 9 in is shown. answer the parts below. make sure you use the correct units in your answers. if necessary, refer to the list of geometry formulas. (a) find the exact surface area of the cylinder. write your answer in terms of π. exact surface area: (b) using the aleks calculator, approximate the surface area of the cylinder. to do the approximation, use the π button on the calculator, and round your answer to the nearest hundredth. approximate surface area:

Explanation:

Step1: Identify radius and height

The base - diameter $d = 6$ in, so the radius $r=\frac{d}{2}=\frac{6}{2}=3$ in, and the height $h = 9$ in.

Step2: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$.

Step3: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. For two bases, $A_{2bases}=2\pi r^{2}=2\pi(3)^{2}=18\pi$ square inches.

Step4: Calculate the lateral surface area

The lateral surface area $A_{lateral}=2\pi rh = 2\pi\times3\times9 = 54\pi$ square inches.

Step5: Calculate the exact surface area

$S=2\pi r^{2}+2\pi rh=18\pi + 54\pi=72\pi$ square inches.

Step6: Calculate the approximate surface area

Using $\pi\approx3.14159$, $S\approx72\times3.14159 = 226.19448\approx226.19$ square inches.

Answer:

(a) $72\pi$ in$^{2}$
(b) $226.19$ in$^{2}$