Question

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

Answer 1

let external and internal radius of the sphere =R and r
R=8/2=4cm
r=4/2=2cm
Let volume of the sphere Vs
diameter of the cone =8=8/2=4cm=radius =R1
let the height of the cone =h
let the volume of the cone =Vc
then, their volume must be equal, since they are melted from the same material.
Vc=Vs
piR1^2h=4/3pi(R^3-r^3)
16h=4/3(4*4*4-2*2*2)
h=64-8/12
h=4.66cm

Answer 2

Answer:

Step-by-step explanation:

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.