Multiple choice

The sum of the height and the radius of a solid cylinder is $35\ cm$ and its total surface area is $3080\ cm^2$; find the volume of the cylinder.

  1. $12,936\ cu. cm$
  2. $12,933\ cu.cm$
  3. $12,930\ cu.cm$
  4. $12,900\ cu. cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given h + r = 35 and 2*pi*r(h + r) = 3080. 2 * (22/7) * r * 35 = 3080. 44 * 5 * r = 3080. 220 * r = 3080, so r = 14. Then h = 35 - 14 = 21. Volume = pi * r^2 * h = (22/7) * 14 * 14 * 21 = 22 * 2 * 14 * 21 = 12,936.

AI explanation

The total surface area formula for a cylinder is 2 times pi times the radius times the sum of the radius and the height. Substituting the known sum of 35 centimeters and the total surface area of 3080 square centimeters gives 2 times 22/7 times the radius times 35 equals 3080; solving this yields a radius of 14 centimeters, meaning the height is 21 centimeters. Applying the volume formula, pi times the square of the radius times the height, the calculation is 22/7 times 14 squared times 21, which results in a volume of 12936 cubic centimeters.

Keep practicing — related questions