Class 10 Math Sample Paper 2019 | Q21B

This 2019 CBSE class 10 Maths 3 mark question is from Surface Areas and Volumes. An easy 3 mark question in CBSE class 10 sample question paper that tests the concept of volume of sphere.

Question 21B: A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find the number of balls.

Video Explanation

Explanatory Answer | 2019 Sample Paper Question 21 Choice 2

Given data

Number of balls = \\frac{\text{Volume of solid sphere}}{\text{Volume of 1 spherical ball}})
Volume of a solid sphere = \\frac{4}{3})× π × r³, where 'r' is the radius of the sphere
Radius of solid sphere = 3 cm
Diameter of each spherical ball = 0.6 cm. So, radius of each small spherical ball = 0.3 cm

Step 1: Compute the volume of the solid sphere and each spherical ball

Volume of solid sphere = \\frac{4}{3}) × π × 3 × 3 × 3 cm³
Volume of 1 spherical ball = \\frac{4}{3}) × π × 0.3 × 0.3 × 0.3 cm³

Step 2: Compute the number of spherical balls that can be recast

Number of balls = \\frac{\text{Volume of solid sphere}}{\text{Volume of 1 spherical ball}}) = \\frac { \frac{4}{3} × π × 3 × 3 × 3 cm^3}{ \frac{4}{3} × π × 0.3 × 0.3 × 0.3 cm^3}) = 1000
1000 spherical balls of 0.6 cm diameter can be recast from a solid sphere of radius 3 cm