Question

a glass cylinder with diameter 20cm has water to a height of 9 CM a metal cube of 8 cm at is immersed in it completely calculate the height of by which water will rise in the cylinder

Answer 1

h = 9cm, r = 20/2 = 10cm, side of cube(a) = 8cm
Total volume of cylinder (after cube was immersed) = Volume of water in cylinder + (Volume of water displaced or volume of cube)
= pi*r2h+a3
=22/7 *102*9+83
=(19800+3584)/7
=23384/7
Now, height of water h1 for this volume can be found by equating pi*r2h1 with this volume:
So, 22/7 *102*h1 = 23384/7
h = 23384/2200 = 10.63 cm
Rise in water level = ​h1​ -h = 10.63-9 = 1.63cm

Answer 2

Answer:

H = 9 cm

diameter = 20 cm so,radius = 10 cm

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