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.
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Answered by
35
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
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
Answered by
29
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
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
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