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The diagram shows the cross-section of e...

The diagram shows the cross-section of eight identical iron balls touching each other on a horizontal surface.

If the volume of a ball is `(9pi)/(2)cm^(3)`, then what should be the minimum length and depth of a box so that all the balls can be placed in it ?

Text Solution

Verified by Experts

Volume of each ball `=(4)/(3)pi r^(3)`
`therefore (4)/(3)pi r^(3)=(9pi)/(2)` (given)
`therefore r^(3)=(27)/(8) rArr r = (3)/(2)` (taking cube root)
`therefore` Diameter of each ball = 3 cm
`therefore` Length `AB=8xx` diameter of ball `=8xx3=24 cm`
and depth of box = diameter of ball = 3 cm.
So, minimum length and depth of box should be 24 cm and 3 cm respectively.
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