Multiple choice

Curved surface area of a cylinder is 753.6 sq. inches. Ratio of radius to height of cylinder is 5 : 6. What is its volume?

  1. 3,632 cu. in

  2. 3,642 cu. in

  3. 3,768 cu. in

  4. 3,832 cu. in
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CSA = 2 * pi * r * h = 753.6. Given r/h = 5/6, let r = 5x and h = 6x. 2 * 3.14 * 5x * 6x = 753.6 => 188.4 * x^2 = 753.6 => x^2 = 4 => x = 2. So r = 10, h = 12. Volume = pi * r^2 * h = 3.14 * 100 * 12 = 3768.

AI explanation

Using the formula for the curved surface area of a cylinder, 2*pi*r*h = 753.6, and given the ratio r:h = 5:6, let r = 5x and h = 6x. Substituting these into the formula gives 2*pi*(5x)*(6x) = 753.6, which simplifies to 60*pi*x^2 = 753.6. Solving for x using pi as 3.14, x^2 equals 4 and x equals 2, meaning the radius is 10 inches and the height is 12 inches. Applying the cylinder volume formula V = pi*r^2*h, the volume is 3.14*10^2*12, which equals 3768 cubic inches.

Keep practicing — related questions