Exams › SSC CGL (Prelims) › General

A cuboidal tank is 12 cm long, 10 cm wide and 6 cm tall. The largest sphere that can fit is dropped into it. Find the volume of the region inside the tank that the sphere does not fill.

1. (720 - 27 pi) cm^3
2. (720 - 36 pi) cm^3
3. (600 - 36 pi) cm^3
4. (720 - 288 pi) cm^3

Correct answer: (720 - 36 pi) cm^3

Solution

The smallest edge (height 6 cm) caps the sphere's diameter, so radius = 3 cm. Box volume = 720 cm^3 and sphere volume = (4/3)pi(3)^3 = 36 pi, so the unoccupied volume is (720 - 36 pi) cm^3.

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