Question

A cube of wood floating in water supports a 200g mass at the centre of its top face. When the mass is removed,the mass rises by 2 cm. Determine the volume of cube.

Answer 1

Let the edge of cube be ℓ. When mass is on the cube of wood


200 g + ℓ3 d wood g = ℓ3 dwater g


⇒ ℓ3 dwood = ℓ3 dwater – 200 … (i)


When the mass is removed


ℓ3 dwood = (ℓ - 2 ) ℓ2 dwater … (ii)


From (i) and (ii)


ℓ3 dwater - 200 = (ℓ- 2) ℓ2 dwater


But dwater = 1


∴ ℓ3 - 200 = ℓ2 (ℓ - 2)


⇒ ℓ = 10 cm

Answer 2

Since the block is a cube, and all three sides are equal. So, you need to find x, the length of the sides. 

You need to know that 1 cm^3 of water has a mass of 1 g. 

Since when the mass is removed, the cube rises 2 cm, that means 2cm height of the block has a mass of 200 gm. 

Now write the equation equating volume to mass: 

200 g = (x^2) (x+2) =x³ +2x² 

x³ + 2x² - 200 = 

Solve this equation for x 

x = 10 cm 

Volume = x³ =1000 cm³
Hope this helps