Question

On increasing the radius of a sphere by 10% find the percentage increase in its volume​

Answer 1

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★ On increasing the radius of a sphere by 10%, find the percentage of increase in its volume .

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★ 33.1 %

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Let the original radius of the sphere be r units

Then, its original volume = (4/3 × π r³)

Radius of the new sphere = (110% of r) units

= (110/100 × r) units

= (11/10 × r) units

Volume of the new sphere = (4/3 π × 11 r/10) cubic units

= (4/3πr ³ × 1331/1000) cubic units

Increase in sphere's volume = {(4/3πr³×1331/1000–4/3πr³)} cubic units

= {(4/3πr³×1331/1000–1)} cubic units

= {4/3πr³×(1331–1000/1000)} cubic units

= {4/3πr³×331/1000} cubic units

Percentage increase in its volume = (4/3πr³×331/10000×100/4/3πr³)%

= (331×100/1000)%

= 33.1%