Multiple choice

Radius and height of a cone are in the ratio 3:4. If its volume is 301.44 cu.in, what will be its lateral surface area?

  1. 156.4 sq.in

  2. 188.4 sq.in

  3. 264.3 sq.in

  4. 423.9 sq.in
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume = 1/3 * pi * r^2 * h = 301.44. With r=3k and h=4k, 1/3 * 3.14 * 9k^2 * 4k = 301.44 => 37.68k^3 = 301.44 => k^3 = 8 => k=2. So r=6, h=8. Slant height l = sqrt(6^2 + 8^2) = 10. Lateral surface area = pi * r * l = 3.14 * 6 * 10 = 188.4.

AI explanation

Let the radius be 3x and the height be 4x, so the volume of the cone formula (1/3 times pi times r squared times h) becomes 1/3 times 3.14 times (3x) squared times 4x, which equals 301.44. Solving this gives x cubed equals 8, so x equals 2; this makes the radius 6 and the height 8. By the Pythagorean theorem, the slant height is the square root of (6 squared plus 8 squared), which is 10. The lateral surface area is pi times r times l, so 3.14 times 6 times 10 equals 188.4 sq in.

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