Question

50. The water level in the cylinder rises by 10 cm
and reaches the brim of the container, when
some water is poured into it. If the ratio of the
volume of water added to the amount of water
already in the container is 5:7, then the height
of the cylinder is
a) 23 cm
b) 24 cm
d) 26 cm
c) 25 cm​

Answer 1

Solution:-

H = 9 cm, diameter = 20 cm so, radius = 10 cm and side of the cube = 8 cm

Total volume of the cylinder (after cube is immersed) = Volume of water in cylinder + Volume of water displaced or volume of the cube

= 22/7*10*10*9 + 8*8*8

= 19800/7 + 512

= 2828.57 + 512

= 3340.57 cu cm

Now, height of water, h1 can be found by equating πr²h1 with this volume.

So,

22/7*10*10*h1 = 3340.57

h1 = (3340.57 × 7)/2200

h1 = 23383.99/2200

Height = 10.63 cm

Rise in the water level in the cylinder = h1 - h

= 10.63 - 9

= 1.63 cm

Answer.