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A toy consists of a cone fixed on top of a hemisphere, both sharing a radius of 36 cm. The height of the cone is 105 cm. What is the total surface area (in cm^2) of the toy?

1. 6025 pi
2. 6588 pi
3. 5799 pi
4. 5240 pi

Correct answer: 6588 pi

Solution

The slant height l = sqrt(36^2 + 105^2) = sqrt(1296 + 11025) = sqrt(12321) = 111 cm. Curved surface of cone = pi * 36 * 111 = 3996*pi. Curved surface of hemisphere = 2*pi*36^2 = 2592*pi. Total = 6588*pi cm^2.

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