UPSC CDS Math Volume and Surface Area Questions

Let the original radius and height of the cone be r units and h units, respectively. New radius of the cone
=R=r−

50

100

×r=

r

2

New height of the cone
=H=h+

200

100

×h=3h
Volume of the original cone=

1

3

πr2h
Volume of the new cone
=

1

3

π(

r

2

)2×3h=

3

4

×

1

3

πr2h
Decrease in volume of the cone
=

1

3

πr2h−

3

4

×

1

3

πr2h
=(1−

3

4

)×

1

3

πr2h
=

1

4

×

1

3

πr2h
Therefore, percentage decrease in volume of the cone
=

1 4 × 1 3 πr2h

1 3 πr2h

×100%=25%