A spherical ball of radius 3 cm is melted and recast into three spheri

1.	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» Let radius of the third ball be r. Volume of the larger ball = \(\frac{4}{3}πR^3\) = \(\frac{4}{3}π{3}^3\) Volume of larger ball = sum of volume of smaller balls ⇒ \(\frac{4}{3}π{3}^3\)= \(\frac{4}{3}π(1.5)^3 +{\frac{4}{3}π(2)^3} + {\frac{4}{3}πr^3}\) ⇒ r³ = 27 – 3.375 – 8 ⇒ r = 2.5 cm

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»

Let radius of the third ball be r.

Volume of the larger ball = \(\frac{4}{3}πR^3\)

= \(\frac{4}{3}π{3}^3\)

Volume of larger ball = sum of volume of smaller balls

⇒ \(\frac{4}{3}π{3}^3\)= \(\frac{4}{3}π(1.5)^3 +{\frac{4}{3}π(2)^3} + {\frac{4}{3}πr^3}\)

⇒ r³ = 27 – 3.375 – 8

⇒ r = 2.5 cm