Question

A glass cylinder with diameter 20 cm has water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder

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.

Answer 2

Answer:

Step-by-step explanation:

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.