Question

There is a cube of edge 8 cm. This cube is immersed in a water-filled vessel with the dimension of its rectangular base (12 cm × 20 cm). By how many cms will the level of water rise in the vessel?

• A. 3.75 cm
• B. 3.13 cm
• C. 2.03 cm
• D. None of these

Hint:

When a solid is immersed in a fluid, the volume of fluid displaced is equal to the volume of the solid. Use this principle along with the area of the base of the vessel to find the rise in water level.

Answer 1

The Correct Option is D

The volume of the cube is: \[ \text{Volume of cube} = \text{edge}^3 = 8^3 = 512 \, \text{cm}^3 \] The area of the base of the vessel is: \[ \text{Area of base of vessel} = 12 \times 20 = 240 \, \text{cm}^2 \] Let the rise in the water level be \( h \). Using the formula for volume: \[ \text{Volume of water displaced} = \text{Area of base of vessel} \times \text{height of water rise} \] \[ 512 = 240 \times h \] Solving for \( h \): \[ h = \frac{512}{240} = 2.13 \, \text{cm} \] Thus, the correct answer is \( 2.13 \, \text{cm} \), but this option is not available, so the correct answer is (d) None of these.