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Question
The base of a rectangular container is a square of side 12 cm. This container holds water up to 2 cm from the top. When a cube is placed in the water and is completely submerged, the water rises to the top and 224 cm3 of water overflows. Find the volume and surface area of the cube.
Solution
When the cube is submerged, the level of water is increased and some water flows out of it.
Volume of the cube
= Volume of water level rise + Volume of water overflown
= 12 x 12 x 2 + 224
= 512cm3
∴ The volume of the cube is 512cm3. ...(Ans 1)
Volume of the cube
= s3
512 = s3
s = `root(3)(512)`
s = 8cm
Surface area of cube
= 6s2
= 6 x 82
= 384cm2
∴ The surface area of the cube is 384cm2. ...(Ans2)
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