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)

Identify Given Information: Identify the given information and the formula for the volume of a cylinder. Volume of a cylinder (V) = πr^2h, where r is the radius and h is the height. Given: V = 108π cm³ and h = 12 cm. We need to find the radius (r) of the cylinder first.Use Volume Formula: Use the volume formula to solve for the radius. 108π = πr^2(12) Divide both sides by π to simplify. 108 = r^2(12)Solve for Radius: Divide both sides by 12 to isolate r^2. 108 / 12 = r^2 9 = r^2Find Surface Area Formula: Take the square root of both sides to solve for r. √9 = r 3 cm = r Now we have the radius of the cylinder.Substitute Values: Identify the formula for the surface area of a cylinder. Surface area (SA) = 2πrh + 2πr^2, where SA is the surface area, r is the radius, and h is the height. We have r = 3 cm and h = 12 cm.Combine Terms: Substitute the values of r and h into the surface area formula. SA = 2π(3)(12) + 2π(3)^2 SA = 2π(36) + 2π(9) SA = 72π + 18πCombine the terms to find the total surface area. SA = 72π + 18π SA = 90π cm² The surface area of the soda can is 90π square centimeters.

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

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Math Problems

Grade 6

Volume of cubes and rectangular prisms: word problems

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Q. A cylindrical soda can has a volume of

108\pi\ \text{cm}^{3}

and a height of

12\text{cm}

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

\newline

Choose

1

answer:

\newline

(A)

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

\newline

(B)

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

\newline

(C)

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

\newline

(D)

90\pi\text{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: $V = 108\pi \, \text{cm}^3$ and $h = 12 \, \text{cm}$ . $\newline$ We need to find the radius $r$ of the cylinder first.
Use Volume Formula: Use the volume formula to solve for the radius. $\newline$ $108\pi = \pi r^2(12)$ $\newline$ Divide both sides by $\pi$ to simplify. $\newline$ $108 = r^2(12)$
Solve for Radius: Divide both sides by $12$ to isolate $r^2$ . $\newline$ $\frac{108}{12} = r^2$ $\newline$ $9 = r^2$
Find Surface Area Formula: Take the square root of both sides to solve for $r$ . $\sqrt{9} = r$ $3 \, \text{cm} = r$ 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 $SA$ is the surface area, $r$ is the radius, and $h$ is the height. $\newline$ We have $r = 3$ cm and $h = 12$ cm.
Combine Terms: Substitute the values of $r$ and $h$ into the surface area formula. $\newline$ $SA = 2\pi(3)(12) + 2\pi(3)^2$ $\newline$ $SA = 2\pi(36) + 2\pi(9)$ $\newline$ $SA = 72\pi + 18\pi$
Combine Terms: Substitute the values of $r$ and $h$ into the surface area formula. $SA = 2\pi(3)(12) + 2\pi(3)^2$ $SA = 2\pi(36) + 2\pi(9)$ $SA = 72\pi + 18\pi$ Combine the terms to find the total surface area. $SA = 72\pi + 18\pi$ $SA = 90\pi \, \text{cm}^2$ The surface area of the soda can is $90\pi$ square centimeters.