Question

A glass cylinde With diameter 20cm has water to a height of 9cm
A metal cube of 8cm edge is immessed in it completely Calculate the height
by which water will rise in the cylinder. (1.62cm).​

Answer 1

AnswEr :

Height by which water will rise in the cylinder is 1.62 cm.

Here, we're given with certain values and dimensions too & we're supposed to find out the height by which water will rise in the cylinder.

GiveN:

• Diameter of the cylinder = 20 cm

• Radius = 2/D = 20/2 = 10 cm

• Height [water level] = 9 cm

• Edge of the Cube = 8 cm

We'll calculate total volume of cylinder in case the cubes are immersed in it. Then, rise in water level in the cylinder.

Accordingly,

$\dashrightarrow$ Volume of the cylinder if cube were immersed = Volume of water present in cylinder + Volume of cube.

$\dashrightarrow$ Volume = πr²h + (side)³

$\dashrightarrow$ Volume = 22/7 × 10 × 10 × 9 + 8 × 8 × 8

$\dashrightarrow$ Volume = 19800/7 + 512

$\dashrightarrow$ Volume = 2828.5 + 512

$\dashrightarrow$ Volume = 3340.5 cm

Now,

$\implies$ Volume [ when cube is immersed ] = πr²h'

$\implies$ 3340.5 = 22/7 × 10 × 10 × h'

$\implies$ h' = 3340.5 × 7 / 10 × 10 × 22

$\implies$ h' = 23383.5/2200

$\implies$ h' = 10.62 cm

Further,

$\longrightarrow$ Rise in water level = h' - h

$\longrightarrow$ Rise in water level = 10.62 - 9

$\therefore$ Rise in water level = 1.62 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