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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 108π 108 \pi cubic centimeters (cm3) \left(\mathrm{cm}^{3}\right) and a height of 12 cm 12 \mathrm{~cm} . What is the surface area of the soda can in square centimeters?\newlineChoose 11 answer:\newline(A) 18πcm2 18 \pi \mathrm{cm}^{2} \newline(B) 36πcm2 36 \pi \mathrm{cm}^{2} \newline(C) 72πcm2 72 \pi \mathrm{cm}^{2} \newline(D) 90πcm2 90 \pi \mathrm{cm}^{2}

Full solution

Q. A cylindrical soda can has a volume of 108π 108 \pi cubic centimeters (cm3) \left(\mathrm{cm}^{3}\right) and a height of 12 cm 12 \mathrm{~cm} . What is the surface area of the soda can in square centimeters?\newlineChoose 11 answer:\newline(A) 18πcm2 18 \pi \mathrm{cm}^{2} \newline(B) 36πcm2 36 \pi \mathrm{cm}^{2} \newline(C) 72πcm2 72 \pi \mathrm{cm}^{2} \newline(D) 90πcm2 90 \pi \mathrm{cm}^{2}
  1. Identify Given Information: Identify the given information and the formula for the volume of a cylinder.\newlineVolume of a cylinder V=πr2hV = \pi r^2 h, where rr is the radius and hh is the height.\newlineGiven volume V=108πcm3V = 108\pi \, \text{cm}^3 and height h=12cmh = 12 \, \text{cm}.\newlineWe need to find the radius rr first.
  2. Volume Formula Calculation: Use the volume formula to solve for the radius rr.108π=πr2(12)108\pi = \pi r^2(12)Divide both sides by π\pi to simplify.108=r2(12)108 = r^2(12)
  3. Radius Calculation: Divide both sides by 1212 to solve for r2r^2. \newline10812=r2\frac{108}{12} = r^2\newline9=r29 = r^2
  4. Surface Area Formula: Take the square root of both sides to find rr. \newline9=r\sqrt{9} = r\newline3cm=r3 \, \text{cm} = r\newlineNow we have the radius of the cylinder.
  5. Substitute Values: Identify the formula for the surface area of a cylinder.\newlineSurface area (SA) = 2πrh+2πr22\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).
  6. Simplify Expression: Substitute the known values into the surface area formula.\newlineSA=2π(3)(12)+2π(3)2SA = 2\pi(3)(12) + 2\pi(3)^2\newlineSA=2π(36)+2π(9)SA = 2\pi(36) + 2\pi(9)
  7. Match Correct Answer: Simplify the expression to find the surface area.\newlineSA=72π+18πSA = 72\pi + 18\pi\newlineSA=90πSA = 90\pi cm2^2
  8. Match Correct Answer: Simplify the expression to find the surface area.\newlineSA=72π+18πSA = 72\pi + 18\pi\newlineSA=90πcm2SA = 90\pi \, \text{cm}^2Match the calculated surface area with the given answer choices.\newlineThe correct answer is (D) 90πcm290\pi \, \text{cm}^2.

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