Question

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

Answer 1

The radius of the larger sphere is 5 cm.

Step-by-step explanation:

Given :

• Weight of the larger sphere = 5920 g.
• Weight of the lighter sphere = 740 g.
• The diameter of lighter sphere = 5 cm.

So, Radius = 2.5 cm

To Find :

The radius of the larger sphere.

Solution :

Consider the :

• The volume of the larger sphere as - 'V1'
• The volume of the lighter sphere as - 'V2'
• Radius of the larger sphere as - 'r1'

∵ The diameter of the lighter sphere is given so the radius is 2.5 cm.

We know that :

$\bigstar\;\boxed{\textbf{Weight of an object = Density} \times \textbf{The volume of that object}}}$

So,

$\implies \dfrac{\textsf{Weight of the heavier sphere}}{\textsf{Weight of the lighter sphere}}\\ \\ \\\implies \dfrac{\sf Density \times V1}{\sf Density \times V2}$

It is given that,

The spheres are made up of same metal.

∴ The ratio of their weights will be equal to the ratio of their volumes.

So,

⇒ (5920/740) = (4/3πr₁³)/(4/3πr³)

⇒ (5920/740) = (4/3 × 22/7× r₁³)/(4/3 × 22/7 × 2.5 × 2.5 × 2.5)

⇒ 8 = r₁³ × 1/2.5 × 1/2.5 × 1/2.5

⇒ 8 = r₁³ × 1/15.625

⇒ r₁³ = 8 × 15.625

⇒ r₁³ = 125

⇒ r₁ = 5 cm.

∴  The radius of the larger sphere is 5 cm.

Answer 2

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