Question

A rectangular container whose base is a square of side 6 cm holds water up to 3 cm from the top. When a solid cube is placed in the water and is completely submerged, the water rises to the top and 17 cm³ of water overflows. Find the edge of the cube.

Answer 1

We have,

A rectangular container whose base is a square of side 6 cm holds water up to 3 cm from the top. When a solid cube is placed in the water and is completely submerged, the water rises to the top and 17 cm of water overflows.

Now we know that,

Volume of a cuboid = (Length) × (Breadth) × (Height)

Then, the volume of a rectangular container is 6 × 6 × 3 = 108 cm³

Now, volume of a cube is (Edge)³

Volume of the cube = The volume of a rectangular container + Volume of water overflows

(Edge)³ = 108 + 17 = 125 cm³

(Edge) = 5 cm

Therefore, the edge of the cube is 5 cm.