The radius of a sphere is 10 cm.

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asked Mar 19 in Class X Maths by priya12 (-11,407 points)

The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume ?

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1 Answer

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answered Mar 19 by muskan15 (-2,499 points)

Volume of sphere = 4/3πr3

∵    Radius = r = 10 cm

∴   Volume of sphere = 4/3π × 10 × 10 × 10

= 4000π/3 cm3

Now, increase the radius 5%

Radius of new sphere = (10 × 105)/100

= 21/2 cm

Volume of new sphere = 4/3π × 21/2 × 21/2 × 21/2

= 9261π/6 cm3

Increase volume = Volume of new sphere – Volume of sphere

= 9261π/6 - 4000π/3

= (9261π - 8000π)/6

= 1261π/6 cm

Percentage of increasing volume = (1261π/6 × 100)/(4000π/3)

= (1261π × 100 × 3)/(4000π × 6) = 1261/80%

= 15 61/80%

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