Multiple choice

Ratio of lateral surface area to the total surface area of a cylinder is 1 : 2. What is the volume of the cylinder if its total surface area is 616 sq. cm?

  1. 1102 cu. cm

  2. 1078 cu. cm

  3. 981 cu. cm

  4. 841 cu. cm

  5. 655 cu. cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

LSA = 2*pi*r*h, TSA = 2*pi*r*h + 2*pi*r^2. Ratio LSA/TSA = 1/2 implies 2*pi*r*h = 2*pi*r^2, so h = r. TSA = 2*pi*r*h + 2*pi*r^2 = 4*pi*r^2 = 616. r^2 = 616 / (4 * 22/7) = 49, so r = 7. Volume = pi*r^2*h = pi*7^2*7 = 22/7 * 49 * 7 = 1078.

AI explanation

The ratio of lateral surface area to total surface area is 2 times pi times r times h divided by 2 times pi times r times (r plus h); setting this ratio to 1:2 reveals that the height equals the radius. Given the total surface area is 616, the formula 2 times pi times r times (r plus r) becomes 4 times pi times r squared equals 616. Substituting 22/7 for pi gives r squared equals 49, so the radius is 7 cm; because the height is also 7 cm, the volume is 22/7 times 7 squared times 7, which equals 1078 cubic cm.

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