Multiple choice

A cone is inscribed in a cylinder such that the base of the cone is equal to the base of the cylinder, and both have the same height. Additionally, the sum of the radius of the base of the cone and the height of the cone is 30 cm. If the total surface area of the cylinder (including both the top and bottom) is 1320 cm2, what is the total capacity (volume) of the cylinder in cubic centimeters?

  1. 1027π

  2. 1127π

  3. 1148π

  4. 1157π

  5. 1172π
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B Correct answer
Explanation

Let r be radius, h be height. r + h = 30. Cylinder surface area = 2*pi*r^2 + 2*pi*r*h = 2*pi*r(r+h) = 1320. 2*pi*r(30) = 1320. r = 1320 / (60*pi) = 22/pi. This leads to h = 30 - 22/pi. The volume is pi*r^2*h. Calculation yields 1127pi.

AI explanation

Let r and h be the radius and height of the cylinder. The total surface area of the cylinder is 2*pi*r*(r + h) = 1320. Since the cone has the same dimensions and r + h = 30, we have 2*pi*r*30 = 1320, giving r = 7 cm and h = 23 cm. The volume of the cylinder is calculated using the formula pi*r^2*h, which equals pi * 7 * 7 * 23 = 1127*pi cubic centimeters.

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