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Question
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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Solution
Volume of sphere = `4/3πr^3`
∴ Radius = r = 10 cm
∴ Volume of sphere = `4/3` π x 10 x 10 x 10
= `(4000π)/3` cm3
Now, increase the radius 5%
Radius of new sphere = `(10 xx 105)/100 = 21/2` cm.
Volume of new sphere = `4/3 π xx 21/2 xx 21/2 xx 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 xx 100)/((4000π)/3)`
= `(1261π xx 100 xx 2)/(4000π xx 6)`
= `1261/80 %`
= `15 61/80 %`
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