Question

A glass cylinder with diamter 20cm has water upto of 9 cm .a metal cube of 8cm edge is immersed in it completly calculate the height by which water will rinse in the cylinder

Answer 1

let h increase in height of water in glass when a metal cube is immersed in water.

change in volume of water , in glass after immerging metallic cube = volume of metallic cube

π r^2 h = (edge length)^3

π(10)^2. h =(8)^3

h =512/100π = 5.12/π = 1.63 cm
hence, in glass increase of level of water is 1.63 cm
so,
new height of water in glass =9 + 1.63
= 10.63 cm

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