Question

The Perimeter of a face of a cube is 20 cm. Find the volume of the cube.

Answer 1

Hint: First find the side of the square of the same perimeter (i.e. 20 cm) then proceed by using the formula to find the volume of a cube (i.e. \[{\text{volume }} = {\text{ }}{\left( {{\text{side}}} \right)^3}\].

Complete step-by-step answer:
Given: The perimeter of the face of the cube is 20 cm.
Step 1: In these types of questions, try to find the side of the shape given. Since, in case of cube, area of face, volume, diagonal, and other related terms can be easily be found by one variable, i.e., side of the cube.
Hence, our first approach is to find the side by the data given.
Step 2: Since every face of cube is a square,
We know that,
Perimeter of square\[ = 4 \times side\]
\[20cm = 4 \times side\]
We get that, \[side = 5cm\]
Step 3: Now, as we have got the side of the cube, we can find out the volume of cube by using the relation,
\[volume = {(side)^3}\]
Step 4:
\[
  volume = {(5)^3} \\
   = 125c{m^3} \\
 \]
Hence, the volume of the cube is \[125c{m^3}\].

Note: In this question, it is important to understand the data given & then try to work out the basic dimension of the given shape. Like, in case of area rather than perimeter, then we would have used \[Area = {(side)^2}\] rather than, \[Perimeter = (4 \times side)\]. Such kinds of questions are common in competitions and exams and questions can be asked for different 3d shapes. Try to memorize the equations of area, perimeter and volume of 3d shapes like cube, cuboid, cone. Try to find a relation between the area of the faces of the object and the volume of the object.