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A cylindrical soda can has a volume of
108 pi cubic centimeters
(cm^(3)) and a height of
12cm. What is the surface area of the soda can in square centimeters?
Choose 1 answer:
(A)
18 picm^(2)
(B)
36 picm^(2)
(c)
72 picm^(2)
(D)
90 picm^(2)

A cylindrical soda can has a volume of $108 \pi$ cubic centimeters $\left(\mathrm{cm}^{3}\right)$ and a height of $12 \mathrm{~cm}$ . What is the surface area of the soda can in square centimeters? $\newline$ Choose $1$ answer: $\newline$ (A) $18 \pi \mathrm{cm}^{2}$ $\newline$ (B) $36 \pi \mathrm{cm}^{2}$ $\newline$ (C) $72 \pi \mathrm{cm}^{2}$ $\newline$ (D) $90 \pi \mathrm{cm}^{2}$

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Scale drawings: word problems

Full solution

Q. A cylindrical soda can has a volume of

108 \pi

cubic centimeters

\left(\mathrm{cm}^{3}\right)

and a height of

12 \mathrm{~cm}

. What is the surface area of the soda can in square centimeters?

\newline

Choose

1

answer:

\newline

(A)

18 \pi \mathrm{cm}^{2}

\newline

(B)

36 \pi \mathrm{cm}^{2}

\newline

(C)

72 \pi \mathrm{cm}^{2}

\newline

(D)

90 \pi \mathrm{cm}^{2}

Identify Given Information: Identify the given information and the formula for the volume of a cylinder. $\newline$ Volume of a cylinder $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height. $\newline$ Given volume $V = 108\pi \, \text{cm}^3$ and height $h = 12 \, \text{cm}$ . $\newline$ We need to find the radius $r$ first.
Volume Formula Calculation: Use the volume formula to solve for the radius $r$ . $108\pi = \pi r^2(12)$ Divide both sides by $\pi$ to simplify. $108 = r^2(12)$
Radius Calculation: Divide both sides by $12$ to solve for $r^2$ . $\newline$ $\frac{108}{12} = r^2$ $\newline$ $9 = r^2$
Surface Area Formula: Take the square root of both sides to find $r$ . $\newline$ $\sqrt{9} = r$ $\newline$ $3 \, \text{cm} = r$ $\newline$ Now we have the radius of the cylinder.
Substitute Values: Identify the formula for the surface area of a cylinder. $\newline$ Surface area (SA) = $2\pi rh + 2\pi r^2$ , where the first term is the lateral surface area and the second term is the area of the two bases (top and bottom).
Simplify Expression: Substitute the known values into the surface area formula. $\newline$ $SA = 2\pi(3)(12) + 2\pi(3)^2$ $\newline$ $SA = 2\pi(36) + 2\pi(9)$
Match Correct Answer: Simplify the expression to find the surface area. $\newline$ $SA = 72\pi + 18\pi$ $\newline$ $SA = 90\pi$ cm $^2$
Match Correct Answer: Simplify the expression to find the surface area. $\newline$ $SA = 72\pi + 18\pi$ $\newline$ $SA = 90\pi \, \text{cm}^2$ Match the calculated surface area with the given answer choices. $\newline$ The correct answer is (D) $90\pi \, \text{cm}^2$ .

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