Multiple choice

The sum of radius of the base and the height of a solid cylinder is $37 m$. If the total surface area of the cylinder be $1628{ m }^{ 2 }$, find the volume.

  1. $4620 cu. m$
  2. $4630 cu. m$
  3. $4520 cu. m$
  4. $4830 cu. m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let r be the radius and h be the height. We have r + h = 37 and 2*pi*r*(r + h) = 1628. Substituting 37 for (r + h), we get 2*pi*r*37 = 1628, so r = 1628 / (74 * pi) which is approximately 7. The volume is pi*r^2*h. Solving the system yields r = 7 and h = 30, so volume = pi * 49 * 30 = 1470 * pi, which is approximately 4620.

AI explanation

Using the given total surface area formula, 2*pi*r(h + r) = 1628, and knowing the sum (h + r) = 37, we can substitute to find the radius: 2*pi*r*37 = 1628, which yields r = 7. Since h + r = 37, the height h is 30. Applying the cylinder volume formula V = pi*r^2*h, we get V = 22/7 * 7^2 * 30 = 4620 cubic meters.

Keep practicing — related questions