Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is
(a)12 cm
(b)14 cm
(c)15 cm
(d)18 cm

Answer 1

Answer:

The Height of the cone is 14 cm.

Among the given options option (b) 14 cm is the correct answer.

Step-by-step explanation:

Given :

Internal diameter of a hollow sphere = 4 cm  

External diameter of a hollow sphere = 8 cm

Diameter of a Cone = 8 cm

Internal radius of a hollow sphere, r = 4/2 = 2 cm

External radius of a hollow sphere, R = 8/2 = 4 cm

Radius of a cone ,r1 = 8/2 = 4 cm

Let h be the height of the cone.

Volume of hollow sphere =  Volume of cone

[Hollow sphere is melted into a cone]  

4/3 π(R³ - r³) = ⅓ πr1²h

4(R³ - r³) = r1²h

4(4³ - 2³) = 4²h

4(64 - 8) = 16h

4 × 56 = 16 h

h = (4 × 56) /16

h = 56/4  

h = 14 cm

Height of the cone = 14 cm

Hence, the Height of the cone is 14 cm.

HOPE THIS ANSWER WILL HELP YOU….

 

Answer 2

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hope the attachment helps you....