Question

A cuboidal shape vessel with dimen-sions $44cm\times 35cm\times 20cm$ is filled with water upto the height of 17 m. A spherical solid metal ball is placed into the vessel; due to this 231 cm${}^3$ water overflows. Find the radius of the ball.

Answer 1

Dimensions of cuboidal vessle $=44cm\times 35cm\times 20cm$
Height of water level $=17cm$
Water displaced from the sphere $=231c{m}^3$
Radius of the ball = ?
Height of the vessel $=20cm$
Height of the empty space $20-17=3$

$\therefore$ Volume of the empty space $=l\times b\times h$
$=44\times 35\times 3$
$=4620c{m}^3$
Volume of the empty space = Volume of the water displaced
$=4620+231$
$=4851c{m}^3$
Volume of the spherical ball $=\frac{4}{3}\pi r^3$
$\therefore 4851=\frac{4}{3}\times \frac{22}{7}\times r^3$
$\therefore r^3=\frac{4851\times 3\times 7}{4\times 22}$
$=\frac{441\times 3\times 7}{4\times 2}$
$\therefore r^3=\frac{441\times 21}{8}$
$\therefore r^3=\frac{9261}{8}$
$\therefore r=\frac{21}{2}=10.5cm$
$\therefore$ Radius of the ball $=10.5cm$.