Question

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Answer 1

Let the radius of third sphere be r₃ 

Volume of big spherical ball=volume of all three balls 

⇒ \(\frac{4}{3}πR^3\)

= \(\frac{4}{3}πr{_1}^3 + \frac{4}{3}πr{_2}^3 + \frac{4}{3}πr{_3}^3\)

⇒ R³ = r₁³ + r₂³ + r₃³ 

⇒ 3 × 3 × 3 = (1.5 × 1.5 × 1.5) + (2 × 2 × 2) + r₃³

⇒ r₃³ = 27 - (3.375 + 8) 

⇒ r₃³ =15.625 

⇒ r_3 ⁼ \(\sqrt[3]{15.625}\)

⇒ r₃ = 2.5 cm