Question

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is
(a)2 cm
(b)3 cm
(c)4 cm
(d)6 cm

Answer 1

Answer:

The height of the Cone is 3 cm

Among the given options option (b) 3 cm is the correct answer.

Step-by-step explanation:

Given :  

Diameter of a solid metallic sphere = 6 cm

Radius of solid metallic square ,r = 6/2 = 3 cm

Diameter of a cone = 12 cm

Radius of solid cone, R = 12/2 = 6 cm

 

Let the height of the Cone be ‘H’ cm.

Volume of solid metallic sphere = Volume of Cone

[solid metallic sphere is melted to form a cone]

4/3 πr³ = 1/3πR²H

4r³= R²H

4 × 3³ = 6² × H

4 × 27 = 36 H

H = (4 × 27)/36

H = 27/9

H = 3 cm

Height of the Cone = 3 cm

Hence, the height of the Cone is 3 cm

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Answer 2

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