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Question
The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: volume
Solution
Let the volume of the sphere be V
Let the new volume of the sphere be V'.
`V=4/3pir^3`
`V^I=4/3pir_1^3`
⇒` V^I=4/3pi((11r)/10^3)`
⇒ `V^I=4/3pi1331/1000 r^3`
⇒`v^I=4/3pir^3 1331/1000 `
⇒`V^I=1331/1000 V`
⇒ `V^I=v+1331/1000v`
`⇒ V^I-v=331/1000 v`
∴ Change in volume=`331/10000 v `
`"Percentage change in volume"="Change in volume"/"original volume" xx100`
=`(331/1000V)/Vxx100`
=`331/10`
= 33.1
Percentage change in volume=33.1%
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