Multiple choice

The ratio between curved surface area and total surface area of a cylinder is $2\,\colon\,3$. If the total surface area be $924\;cm^2$, find the volume of the cylinder.

  1. $2156\;cm^3$
  2. $1256\;cm^3$
  3. $1265\;cm^3$
  4. $1862\;cm^3$
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A Correct answer
Explanation

CSA/TSA = 2pi*r*h / (2pi*r*h + 2pi*r^2) = h / (h+r) = 2/3. So 3h = 2h + 2r, h = 2r. TSA = 2pi*r(h+r) = 2pi*r(3r) = 6pi*r^2 = 924. pi*r^2 = 154. r^2 = 154 * 7/22 = 49, r = 7. h = 14. Volume = pi*r^2*h = (22/7) * 49 * 14 = 22 * 7 * 14 = 2156.

AI explanation

The formula for curved surface area is 2 pi r h and for total surface area is 2 pi r (h+r). Given their ratio is 2:3, we get h divided by the quantity h+r equals 2/3, which means the height is twice the radius. Using the total surface area of 924, we solve 2 pi r (3r) equals 924 to find r equals 7 cm and h equals 14 cm. The volume of the cylinder, pi r squared h, is 22/7 times 49 times 14, giving 2156 cubic cm.

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