Question

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

Answer 1

Given that a spherical ball of radius 3 cm

We know that Volume of a spher `= 4/3pir^3`

So its volume(v) `= 4/3pi(3)^3`

Given that ball is melted and recast into three spherical balls

Radii of first ball (v₁) = `4/3pi(1.5)^3`

Radii of second ball(v₂) = `4/3pi(2)^3`

Radii of third ball ______?

Volume of third ball `= 4/3pir^3 = v_3`

Volume of spherical ball is equal to volume of 3 small spherical balls

⇒ `4/3pir^3 + 4/3pi(1.5)^3 + 4/3pi(2)^3 = 4/3pi(3)^3`

⇒ `r^3+(1.5)^3+(2)^3 = (3)^3`

⇒ `r^3 = 3^3-1.5^3-2^3`

⇒ `r-(15.6)1/3`

⇒ `r = 2.5  cm`

Diameter (d) = 2r = 2 × 2.5 = 5 cm

∴ Diameter of third ball = 5 cm