A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is:
a. 4.2 cm
b. 2.1 cm
c. 2.4 cm
d. 1.6 cm

Solution:

Given, the height of the cone is 8.4 cm

Base radius is 2.1 cm

The cone is melted and recast into a sphere.

We have to find the radius of the sphere.

Volume of the cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Here, r = 2.1 cm and h = 8.4 cm

Now, volume of cone = 1/3 π(2.1)²(8.4)

= 1/3 π(4.41)(8.4)

= π(1.47)(8.4) cm³

Volume of sphere = 4/3 πr³

Where, r is the radius of the sphere

Let the radius of the sphere be R

Volume of sphere = 4/3 πR³

Given, volume of cone = volume of sphere

So, 4/3 πR³ = π(1.47)(8.4)

4/3 R³ = 1.47 × 8.4

1/3 R³ = 1.47 × 2.1

R³ = 1.47 ×  2.1 × 3

R³ = 9.261

Taking cube root,

R = 2.1 cm

Therefore, the radius of the sphere is 2.1 cm

✦ Try This: A cone is 9 cm high and the radius of its base is 3 cm. It is melted and recast into a sphere. The radius of the sphere is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.1 Problem 3

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is: a. 4.2 cm, b. 2.1 cm, c. 2.4 cm, d. 1.6 cm

Summary:

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is 2.1 cm

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