UPSC CDS 1 2022 Math Paper

Given:
The radius and height of a right circular cone are in the ratio 3:7
The volume of the cone is 528cm3
Concept used:
Volume of a right circular cone =(1∕3)πr2h
r= radius, h= height
Calculation:
Let the radius and height of the cone be 3y and 7y
Now, volume of the cone =(1∕3)π(3y)2×7y
According to the question,
‌

1

3

×‌

22

7

×(3y)2×7y=528
⇒‌

1

3

×‌

22

7

×9y2×7y=528
⇒66y3=528cm3
⇒6y3=48cm3
⇒y3=8cm3
⇒y=2cm
So, the height of the cone =7y=7×2=14
∴ The height of the cone is 14cm.