Maths-
General
Easy
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 a cuboidal solid piece of metal. It is melted and converted into a cube. We have to find the dimensions of the cube. The shape of the solid piece of metal is changed. But as it's melted and changed into different shape, the volume of the solid piece remains constant. We will use this property to find the dimensions of cube.
The correct answer is: 12 cm
The dimensions of the solid metal cuboid are as follows:
lenth = 24 cm
heigt = 18cm
breadth = 4cm
The volume of the solid metal piece will remain constant. So, we will find the volume of metal piece using the dimensions of cuboid. Then, we will equate it with the volume of cube.
Volume of cuboid = length × breadth × height
= 24 × 18 × 4
= 1728cm3
We will equate this value with volume of cube
Volume of cube = (side)3
1728 = (side)3
Rearranging we get,
(side)3 = 1728
Taking cube root of both the sides
side = 12
So, the length of the side of cube is 12cm.
For such questions, we should know the formulas of volume of different shapes. We have to remember that when any metal piece is melted, it's volume doesn't change. The change is there only in the dimensions of the metal piece.
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