Multiple choice

The radius and the height of a cylinder are in the ratio 2 : 1. The radius is increased by 50% and the height by 100%. If the sum of the original and the new volume is 23,716 cm3, find the lateral surface area of the cylinder.

  1. 516 cm2

  2. 616 cm2

  3. 626 cm2

  4. 636 cm2

  5. 716 cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Let the original height be 2x and radius be x, making the original volume pi * x^2 * 2x = 2 * pi * x^3. The new height is 4x and the new radius is 1.5x, so the new volume is pi * (1.5x)^2 * 4x = 9 * pi * x^3. Since 11 * pi * x^3 = 23716, x^3 equals 686. The lateral surface area is 2 * pi * r * h = 2 * (22/7) * 7 * 14 = 616 sq cm.

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