Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
a. 4 cm
b. 3 cm
c. 2 cm
d. 6 cm

Solution:

It is given that

Diameter of cylinder = 2 cm

Radius of cylinder = 2/2 = 1 cm

Height of the cylinder = 16 cm

We know that

Volume of cylinder = πr²h

Substituting the values

Volume of cylinder = π × 1² × 16 = 16π cm

Consider r cm as the radius of solid sphere

Volume = 4/3 πr³

From the question

Volume of twelve solid spheres = Volume of cylinder

12 × 4/3 πr³ = 16π

By further calculation

r³ = 1

Taking cube root on both sides

r = 1 cm

So the diameter = 2 × 1 = 2 cm

Therefore, the diameter of each sphere is 2 cm.

✦ Try This: Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 4 cm and height 18 cm. The diameter of each sphere is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.1 Problem 12

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is a. 4 cm, b. 3 cm, c. 2 cm, d. 6 cm

Summary:

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is 2 cm

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