Multiple choice

The height of a right circular cone is 35 cm and the area of its curved surface is four times the area of its base. What is the volume of the cone (in 10-3 m3 and correct up to three decimal places)?

  1. 3.316

  2. 3.384

  3. 2.994

  4. 2.625
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C Correct answer
Explanation

Curved surface area = pi * r * l = 4 * (pi * r^2) => l = 4r. l^2 = r^2 + h^2 => (4r)^2 = r^2 + 35^2 => 15r^2 = 1225 => r^2 = 81.66 => r = 9.037. Volume = (1/3) * pi * r^2 * h = (1/3) * pi * 81.66 * 35 = 2994.4 cm^3 = 2.994 * 10^-3 m^3.

AI explanation

Using the given relationship pi * r * l = 4 * pi * r^2, we find the slant height l = 4r. Applying the Pythagorean theorem, h^2 + r^2 = l^2 gives 35^2 + r^2 = (4r)^2, so 1225 = 15r^2, meaning r^2 = 245/3 and r = sqrt(245/3) cm. The volume is (1/3) * pi * r^2 * h = (1/3) * (22/7) * (245/3) * 35, which equals (22/9) * 1225 = 2994.444 cubic cm. Converting this to 10^-3 cubic meters by multiplying by 10^-3 gives 2.994.

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