Multiple choice

The total surface area of a solid cylinder is $616$ $cm^2$. If the ratio between its curved surface area and total surface area is $1 : 2$; find the volume of the cylinder.

  1. $1078$ cu. cm
  2. $1070$ cu.cm
  3. $1700$$ cu.cm
  4. $1087$ cu. cm
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A Correct answer
Explanation

Total Surface Area (TSA) = 2*pi*r*(r+h) = 616. Curved Surface Area (CSA) = 2*pi*r*h. Given CSA/TSA = 1/2, then CSA = 308. Thus 2*pi*r*h = 308 and 2*pi*r^2 = 308. From 2*pi*r^2 = 308, r^2 = 49, so r = 7. Then 2*pi*7*h = 308 gives h = 7. Volume = pi*r^2*h = (22/7)*49*7 = 1078.

AI explanation

Given the ratio of curved surface area to total surface area is 1:2, the curved surface area must be half of the total surface area, which is 308 square centimeters. Using the formula for curved surface area, 2 times pi times the radius times the height equals 308, and the formula for total surface area gives 2 times pi times the radius times the sum of radius and height equals 616; dividing the two equations reveals the radius equals the height. Solving 2 times 22/7 times the radius squared equals 308 gives a radius and height of 7 centimeters each. The volume formula, pi times the radius squared times the height, gives 22/7 times 7 squared times 7, resulting in 1078 cubic centimeters.

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