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The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1% approximately.

Solution:

Given, radius of sphere is increased by 10%

We have to prove that the volume will increase by 33.1%.

Where, r is the radius of the sphere

Given, r = r + 10%r

= r + 10/100 r

= 110/100 r

Increased radius = 11/10 r

Increased volume = 4/3 π(11/10 r)³

= 4/3 π(1331/1000)r³

= 4/3 π(1.331)r³

= 1.331(4/3 πr³)

Increase in volume = increased volume - old volume

= 1.331(4/3 πr³) - (4/3 πr³)

= (1.331 - 1)(4/3 πr³)

= 0.331(4/3 πr³)

Percentage increase in volume = (increase in volume / old volume) × 100

= [0.331(4/3 πr³) / (4/3 πr³)] × 100

= 0.331 × 100

= 33.1%

Therefore, it is proved that the volume will be increased by 33.1% approximately.

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

✦ Try This: If the radius of a sphere is doubled, then its volume is increased by what percent?

NCERT Exemplar Class 9 Maths Exercise 13.3 Sample Problem 2

Summary:

The radius of a sphere is increased by 10%. It is proven that the volume will be increased by 33.1% approximately

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