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Q.

If we have a hemisphere shaped lead of radius 9 cm and we want to convert it into a right circular cone with height 72 cm, what will be the radius of the cone produced?

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a

5 cm

b

8 cm

c

4.5 cm

d

6 cm

answer is C.

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Detailed Solution

We are given a hemisphere shaped lead of radius 9 cm and we want to convert it into a right circular cone with height 72 cm.
We already know that the volume of the cone is

13 π r 2 h,

where r is the radius of the cone and h is the height of the cone.
The volume of the hemisphere is

23 π R 3,

where R is the radius of the hemisphere.
If we let the radius of the base of the cone as r, then we can calculate it as follows,
Volume of right circular cone = Volume of hemisphere shaped lead.

⇒ 13 × π × r 2 × h = 23 × π × R 3 ⇒ 13 × π × r 2 × 72 = 23 × π × 93 ⇒ r 2 = 23 × π × 729 13 × π × 72 ⇒ r 2 = 145872

Simplifying the radius,

Therefore, the radius of the base of the cone will be 4.5 cm.
Hence, option (3) is correct.

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