Question

The diameters of three solid balls of iron are 6 cm, 8 cm and 10 cm. They are melted and recast a solid ball. Find the diameter of this ball.

Answer 1

Radius of first ball `r_(1)=(6)/(2)=3 cm`
Radius of second ball `r_(2)=(8)/(2)=4 cm`
Radius of third ball `r_(3) = (10)/(2)=5 cm`
Let radius of new ball = r
Now, volume of new ball = sum of the volumes of three balls
`rArr (4)/(3)pi r^(3)=(4)/(3)pi r_(1)^(3)+(4)/(3)pi r_(2)^(3)+(4)/(3)pi r_(3)^(3)`
`rArr r^(3)=r_(1)^(3)+r_(2)^(3)+r_(3)^(3)`
`= 3^(3)+4^(3)+5^(3)`
= 27 + 64 + 125
= 216
`rArr r = 6`
`therefore` Diameter of new ball `= 2xx6 =12 cm`