Multiple choice

A right circular cylinder has a diameter of 20 cm and its curved surface area is 1000 cm2. What is the volume of the cylinder?

  1. 4000 cm3

  2. 4500 cm3

  3. 5000 cm3

  4. 5200 cm3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area = 2 * pi * r * h = 1000. Diameter = 20, so r = 10. 2 * pi * 10 * h = 1000, so h = 1000 / (20 * pi) = 50/pi. Volume = pi * r^2 * h = pi * 100 * (50/pi) = 5000.

AI explanation

Using the formula for the curved surface area of a cylinder, 2*pi*r*h equals 1000. Substituting the radius of 10 cm gives 20*pi*h equals 1000, so the height is 50 divided by pi. Applying the volume formula V equals pi multiplied by the square of the radius multiplied by the height, the volume becomes pi multiplied by 100 multiplied by 50 divided by pi, which results in 5000 cubic cm.

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