Question

A cylindrical glass tube with radius 10 cm has water upto height 9 cm. A metal cube of 8 cm edge is immersed in it completely. By how much cm the water level rise in the glass tube?

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


hope this helps......

Answer 2

Radius of tube = 10 cm

Edge of cube = a = 8 cm

So ,

Vol of cube = vol of cylinder

a^3 = πr^2h

(8)^3 = 3.14 * 10 * 10 * h

512 = 314 *h

h = 512 / 314

h = 1.63 cm