Question

The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: volume

Answer 1

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%