Question

Please find my question attached below

Answer 1

Answer:

Water level will rise by 0.5 m

Step-by-step explanation:

This is a very Good Question,

We can do it in a general way and in a calculated way,

We have,

Length = 4m

Height = 5m

Water Filled Height = 2.5m

Since it has a square base, it's length and breadth must be equal,

So,

Breadth = 4m

1st Method (General way)

Let the length be L, Breadth be B and Water filled Height be H,

And let the new Height after rising be H'

So,

Volume of water in the tank before dropping the cube = L × B × H

= LBH

Now, the cube is dropped, so Volume must increase.

Volume of cube = (Side)³

= (2)³

= 8 m³

Hence,

The new Volume of the tank = (LBH + 8)m³

But after the cube is dropped water level will rise so the new Volume must be

= L × B × H'

= LBH'

Then, they have to be equal right,

So,

LBH + 8 = LBH'

LBH' - LBH = 8

Taking LB common,

LB(H' - H) = 8

Now let's substitute the values,

(4)(4)(H' - H) = 8

(H' - H) = 8/16

(H' - H) = (1/2) = 0.5 m

∴ Difference in Height = 0.5 m

∴ Water level will rise by 0.5 m

2nd Method (Calculations)

Volume of water in the tank before dropping the cube = L × B × H

= 4 × 4 × 2.5

= 40 m³

Now, the cube is dropped,

Then, Volume must increase.

Volume of cube = (Side)³

= (2)³

= 8 m³

Hence,

The new Volume of the tank = (40 + 8)m³

= 48 m³

But after the cube is dropped water level will rise

Let the new Height be x

So,

The new Volume must be

= L × B × x

= (4)(4)x

= 16x m³

Then, they have to be equal right,

So,

48 = 16x

x = 48/16

x = 3m

Hence,

Water level will rise from 2.5 to 3 m.

∴ Difference in Height = 3 - 2.5

= 0.5m

∴ Water level will rise by 0.5 m

Hope it helped you and believing you understood it....All the best