Question

A sphere of radius 14 cm is melted and cast into a number of tiny cones of radius 2.33 cm each and height 6 cm. Find the number of cones that will be formed?

(a) 726

(b) 816

(c) 721

(d) 821

This question was posed to me in an international level competition.

Query is from Conversion of Solid from One Shape to Another topic in portion Surface Area and Volumes of Mathematics – Class 10

Answer 1

The correct option is (d) 821

Easy explanation: Number of cones(volume of a cone) = volume of sphere

number of cones(\(\frac {1}{3}\)πr^2h) = \(\frac {4}{3}\)πr^3

number of cones(\(\frac {1}{3}\) × 3.14 × 2.33^2 × 6) = \(\frac {4}{3}\) × 3.14 × 14^3

number of cones(14) = 11488.21

number of cones = 821