Explain the question using various formulas.
Class 10th Cbse, RD Sharma.
Surface area and volumes
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3. A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two balls are 2 cm and 1.5 cm, respectively. Determine the diameter of the third ball.
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Solution:
Given,
The radius of the spherical ball = 3 cm
We know that,
The volume of the sphere = 4/3 πr3
So, its volume (V) = 4/3 πr3
That the ball is melted and recast into 3 spherical balls.
Volume (V1) of first ball = 4/3 π 1.53
Volume (V2) of second ball = 4/3 π23
Let the radius of the third ball = r cm
Volume of the third ball (V3) = 4/3 πr3
Volume of the spherical ball is equal to the volume of the 3 small spherical balls.
Now,
Cancelling out the common part from both sides of the equation, we get
(3)3 = (2)3 + (1.5)3 + r3
r3 = 33– 23– 1.53 cm3
r3 = 15.6 cm3
r = (15.6)1/3 cm
r = 2.5 cm
As diameter = 2 x radius = 2 x 2.5 cm
= 5.0 cm.
Thus, the diameter of the third ball is 5 cm.