A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is
a. 21cm
b. 23cm
c. 25cm
d. 19cm

Solution:

We know that

Volume of cuboid = lbh

Where l is the length

b is the breadth

h is the height

It is given that

l = 49 cm

b = 33 cm

h = 24 cm

Substituting the values in the formula

Volume of cuboid = 49cm × 33cm × 24cm = 38808 cm³

Consider r as the radius of the cube

We know that

Volume of sphere = 4/3 πr³

Where r is the radius of sphere

Here

Volume of cuboid = Volume of sphere molded

38808 = 4/3 πr³

By further calculation

πr³ = 29106

r³ = 29106/(22/7)

So we get

r³ = 9261

Taking cube root on both sides

r =∛9261 = 21

Therefore, the radius of the sphere is 21 cm.

✦ Try This: A solid piece of iron in the form of a cuboid of dimensions 50cm × 30cm × 20cm, is moulded to form a solid sphere. The radius of the sphere is

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

NCERT Exemplar Class 10 Maths Exercise 12.1 Problem 10

A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is a. 21cm, b. 23cm, c. 25cm, d. 19cm

Summary:

A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is 21 cm

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