A cylindrical soda can has a volume of 108π cubic centimeters (cm3) and a height of 12cm. What is the surface area of the soda can in square centimeters?Choose 1 answer:(A) 18πcm2(B) 36πcm2(C) 72πcm2(D) 90πcm2
Q. A cylindrical soda can has a volume of 108π cubic centimeters (cm3) and a height of 12cm. What is the surface area of the soda can in square centimeters?Choose 1 answer:(A) 18πcm2(B) 36πcm2(C) 72πcm2(D) 90πcm2
Identify Given Information: Identify the given information and the formula for the volume of a cylinder.Volume of a cylinder V=πr2h, where r is the radius and h is the height.Given volume V=108πcm3 and height h=12cm.We need to find the radius r first.
Volume Formula Calculation: Use the volume formula to solve for the radius r.108π=πr2(12)Divide both sides by π to simplify.108=r2(12)
Radius Calculation: Divide both sides by 12 to solve for r2. 12108=r29=r2
Surface Area Formula: Take the square root of both sides to find r. 9=r3cm=rNow we have the radius of the cylinder.
Substitute Values: Identify the formula for the surface area of a cylinder.Surface area (SA) = 2πrh+2πr2, 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.SA=2π(3)(12)+2π(3)2SA=2π(36)+2π(9)
Match Correct Answer: Simplify the expression to find the surface area.SA=72π+18πSA=90π cm2
Match Correct Answer: Simplify the expression to find the surface area.SA=72π+18πSA=90πcm2Match the calculated surface area with the given answer choices.The correct answer is (D) 90πcm2.