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The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.

Solution:

Given, the ratio of the volume of two spheres is 64 : 27

We have to find the ratio of their surface areas.

Where, r is the radius of the sphere

Volume of first sphere = 4/3 πr³

Volume of second sphere = 4/3 πR³

Given, 4/3 πr³ : 4/3 πR³ = 64 : 27

r³ : R³ = 64 : 27

r : R = 4 : 3

Now, radius of first sphere, r = 4 units

Radius of second sphere = 3 units

Surface area of sphere = 4πr²

Where, r is the radius of the sphere

Surface area of first sphere = 4π(4)²

= 4π(16)

= 64π square units

Surface area of first sphere = 4π(3)²

= 4π(9)

= 36π square units

Ratio of surface area = 64π : 36π

= 64 : 36

= 16 : 9

Therefore, the ratio of the surface area is 16 : 9

✦ Try This: The volumes of the two spheres are in the ratio 125 : 64. Find the ratio of their surface areas.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.4 Problem 5

Summary:

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

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