Multiple choice

A cylinder has a surface area of 360$\pi$ units square, and is 3 units tall. What is the diameter of the cylinder's circular base ?

  1. $24$ units
  2. $36$ units
  3. $32$ units
  4. $18$ units
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of cylinder = 2*pi*r*h + 2*pi*r^2 = 360*pi. Given h = 3, 6*pi*r + 2*pi*r^2 = 360*pi. Dividing by 2*pi: r^2 + 3r - 180 = 0. (r+15)(r-12) = 0. r = 12. Diameter = 2r = 24.

AI explanation

The surface area of a cylinder is calculated as 2 times pi times r squared plus 2 times pi times r times h. Setting this equal to 360 times pi with a height of 3 gives 2 times pi times r squared plus 6 times pi times r equals 360 times pi, and dividing by 2 times pi yields r squared plus 3r minus 180 equals 0. Factoring this gives (r plus 15) times (r minus 12) equals 0, so the radius is 12 and the diameter is 24 units.

Keep practicing — related questions