UPSC CDS Math Volume and Surface Area Questions

Let r and h be the radius and height of the right circular cone respectively.
Radius of the new cone
=r+

p

100

r=r(1+

p

100

)
Increase in volume of the cone
=‌‌

1

3

πr2h[(1+‌‌

p

100

)2−1]
=‌‌

1

3

πr2h[(‌‌

p

100

)2+‌‌

2p

100

]
Therefore, percentage increase in the volume of the cone
=p(2+‌‌

p

100

)%