Multiple choice

The total surface area of a solid cylinder is $462{cm}^{2}$. Its curved surface area is one third of total surface area. Find the volume of the cylinder.

  1. $229\ cm^3$
  2. $509\ cm^3$
  3. $439\ cm^3$
  4. $539\ cm^3$
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D Correct answer
Explanation

TSA = 462, CSA = 1/3 * 462 = 154. TSA = CSA + 2 * pi * r^2, so 462 = 154 + 2 * pi * r^2 => 2 * pi * r^2 = 308 => r^2 = 308 * 7 / 44 = 49 => r = 7. CSA = 2 * pi * r * h = 154 => 2 * (22/7) * 7 * h = 154 => 44h = 154 => h = 3.5. Volume = pi * r^2 * h = (22/7) * 49 * 3.5 = 22 * 7 * 3.5 = 539.

AI explanation

The curved surface area is one-third of 462, which equals 154 square cm, meaning the combined area of the two circular bases is 462 minus 154, or 308 square cm. Since the two bases make up 2 pi r squared, we have 2 pi r squared equals 308, yielding a radius squared value of 49 and a radius of 7 cm. Using the curved surface area formula, 2 pi r h equals 154, so 2 times (22/7) times 7 times h equals 154, which gives a height of 5 cm. The volume of the cylinder is pi r squared h, which is (22/7) times (7 squared) times 5, resulting in 539 cubic cm.

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