Question

Soumya took two right circular cones of the same vertical height. One of the two cones is a solid one, while the other is hollow from inside. By measuring the cross-sectional areas of the cones and from the knowledge of symmetry, by using suitable formulas, he found the positions of the centre of gravity of both cones. He found that the difference is about 1.5 cm. What is the vertical height of the two cones?

Answer 1

For a uniform solid cone, the centre of gravity is at a height of `h/4` from the base.

For a thin hollow cone, it is at a height of `h/3` from the base.

The difference between these positions is `h/3 − h/4 = h/12`.

Since this difference is 1.5 cm, `h/12` = 1.5 cm, so h = 18 cm.

Therefore, the vertical height of each cone is 18 cm.