Question

Spherical Marbles of diameter 1.4 cm. are dropped into a cylindrical beaker of diameter 7 cm., which contains some water. Find the number of marbles that should be dropped in to the beaker, so that water level rises by 5.6 cm​

Answer 1

Given:

diameter of marbles = 1.4cm

diameter of cylindrical beaker = 7cm

water level risen by = 5.6cm

To find:

number of marbles that should be dropped into the water.

solution:

radius of marble = $\frac{1.4}{2}=0.7cm$

volume of one marble = $\frac{4}{3} \pi (0.7)^{3}$

                                     =$\frac{4}{3} \pi$× $0.343 = \frac{1.372}{3} \pi cm^{3}$

radius of beaker =$\frac{7}{2}= 3.5cm$

hieght of water level raised= 5.6cm

volume of raised water in beaker=$\pi (3.5)^{2}$×$5.6=68.6 \pi cm^{2}$

required number of marbles= $\frac{volume of raised water in beaker}{volume of one marble}$

                                              =$\frac{68.6\pi }{1.372\pi }$×$3=150$

therefore, 150 marbles should be added to the beaker for the water level to rise by 5.6cm.