Question
A so lid piece of metal in the form of a Cuboid of dimes ions 24 cm x 18 cm x 4 cm is melted down and casted into a cube Find length of each edge of cube.
- 12 cm
- 22 cm
- 20 cm
- none of these
Hint:
We are given the dimensions of solid metal piece of cuboid. It is melted and converted into a cube. We have to find the dimensions of the cube. This question is about volume of cuboid. Even when the shape is changed the volume remains constant.
The correct answer is: 12 cm
The dimensions of the solid piece of metal are 24cm × 18cm × 4cm.
It is melted and converted into a cube. So, we can that the volume of the solid piece of metal is constant.
We are asked to find the dimensions of a cube formed from the metal piece.
We will first find the volume of cuboid.
Volume = length × breadth × height
= 24 × 18 × 4
= 1728 cu. cm
Let’s us consider the side of cube to be “x”.
Volume of cube = (side)3
= x3
Comparing both the volumes
x3 = 1728
Taking cube roots
x = 12 cm
Therefore, the length of the cube is 12 cm.
For such questions, we should know formula of volumes of different shapes.
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