Question

A hollow sphere of internal and external diameters 4 and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.

Answer 1

Answer:

The height of the cone  is 14 cm.

Step-by-step explanation:

SOLUTION :  

Given :  

Internal diameter of hollow sphere = 4 cm

Internal radius of hollow sphere , r = 2 cm

External diameter of hollow sphere = 8 cm

External radius of hollow sphere , R = 4 cm

Diameter of the cone = 8 cm

Radius of the cone , r1 = 4 cm

Volume of the hollow spherical shell = 4/3π(R³ − r³)

Let the height of the cone be h cm.

Volume of the cone = 1/3πr1²h

Since, the hollow spherical shell is melted into a cone , so volume of both are equal

Volume of the hollow spherical shell = Volume of the cone

4/3π(R³ − r³) = 1/3πr1²h

4(R³ − r³) = r1²h

4(4³ - 2³) = 4²h

4(64 - 8) = 16h

4(56) = 16h

h = (4 × 56) /16

h = 56/4 = 14

h = 14 cm

Hence, the height of the cone  is 14 cm.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

Step-by-step explanation:

V.OF SPHERE=4/3 PIE ( R cube - r cube)  

And v.of cone=1/3 pie R square h.

V.of sphere = v.of cone.

4/3*22/7*(4*4*4-2*2*2)=

1/3*22/7*4*4*4h

4(64-8)=16*h

4*56=16*h

h=(4*56)/16

h=14 cm. ANS