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Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Solution:

Given, two solid spheres are made of the same metal

The metal spheres have weights 5920 g ad 740 g

The diameter of the smaller one is 5 cm

We have to find the radius of the larger sphere

We know, density = mass / volume

So, volume = mass / density

Volume of small sphere = mass of small sphere / density

Vₛ = 740/density -------------------- (1)

Volume of large sphere = mass of large sphere / density

Vₗ = 5920/density ----------------- (2)

On dividing (1) and (2),

Vₗ/Vₛ = (5920/density) / (740/density)

= 5920/740

= 592/74

= 8

Volume of sphere = 4/3 πr³

Given, radius of small sphere = 5/2 = 2.5 cm

Volume of small sphere, Vₛ = 4/3 π(2.5)³

Volume of large sphere, Vₗ = 4/3 πr³

Now, (4/3 πr³) / (4/3 π(2.5)³) = 8

r³/(2.5)³ = 8

r³ = (2.5)³8

r³ = (2.5)³(2)³

Taking cube root,

r = 2.5(2)

r = 5 cm

Therefore, the radius of the large sphere is 5 cm

✦ Try This: Two solid spheres made of the same metal have weights 5800 g and 200 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 4 cm.

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

NCERT Exemplar Class 9 Maths Exercise 13.3 Problem 5

Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Summary:

Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. The radius of the larger sphere, if the diameter of the smaller one is 5 cm is 5 cm

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