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A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed

Solution:

Given, a solid metallic sphere of radius 10.5 cm

Sphere is melted and recast into a number of smaller cones each of radius 3.5 cm

and height 3 cm.

We have to find the number of cones so formed.

Volume of sphere = (4/3)πr³

= (4/3)π(10.5)³

= 1543.5π cm³

Volume of the cone = (1/3)πr²h

= (1/3)π(3.5)²(3)

= 12.25π cm³

Number of small cones = volume of sphere/volume of cone

= 1543.5π/12.25π

= 126

Therefore, the number of smaller cones so formed is 126.

✦ Try This: A solid metallic sphere of radius 12 cm is melted and recast into a number of smaller spheres, each of radius 2 cm. Find the number of spheres so formed.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.3 Sample Problem 2

A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed

Summary:

A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. The number of cones so formed is 126

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