Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
a. 3 : 4
b. 4 : 3
c. 9 : 16
d. 16 : 9

Solution:

Consider r1 and r2 as the radius of two spheres

The ratio of volumes of two spheres is 64: 27

We know that

Volume of sphere = 4/3 π r³

Here

V1/V2 = 64/27

4/3 π r1³/ 4/3 π r2³ = 64/27

By further simplification

(r1/r2)³ = (4/3)³

Taking cube root on both sides

r1/r2 = 4/3

Consider S1 and S2 as the surface areas of the two spheres

S1/S2 = 4πr1²/4πr2² = (r1/r2)²

Here

S1: S2 = (4/3)² = 16/9

Therefore, the ratio of their surface areas is 16: 9.

✦ Try This: Volumes of two spheres are in the ratio 125:8. The ratio of their surface areas is

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

NCERT Exemplar Class 10 Maths Exercise 12.1 Problem 20

Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is a. 3 : 4, b. 4 : 3, c. 9 : 16, d. 16 : 9

Summary:

Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is 16: 9

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