Question

Marbles of radius 0.7 cm are dropped into a cylindrical beaker of diameter 7 em containing some
water. Find the mumber of marbles that can be dropped into the beaker so that the water level rises by
5.6 cm

Answer 1

150 marbles

Step-by-step explanation:

For this we will have to take out the volume of the cylinder and the marbles

volume of cylinder= πr^2h

d=7cm

therfore, r=7/2cm

h= 5.6cm= 56/10

therefore, the volume of cylinder=

22/7×(7/2)^2×56/10

22/7×49/4×56/10

(22×49×56)/(7×4×10)(just cancel out)

(11×7×14)/5

1078/5cm^3

volume of sphere=4/3πr^3

r=0.7= 7/10

therefore, the volume of each marble=

4/3×22/7×(7/10)^3

4/3×22/7×343/1000

(4×22×343)/(3×7×1000)(cancelling)

(22×49)/(3×250)(again cancel)

(11×49)/(3×125)

539/375cm^3

NUMBER OF MARBLES NEEDED=

volume of cylinder/volume of marble

1078/5÷539/375

1078/5×375/539(cancel)

2×75

150 marbles