
The perimeter of one face of a cube is 24 cm. Find the volume of the cube .
Answer
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Hint: Here, we will assume the length of the side of the cube to be equal to ‘a’. After this we will try to calculate the value of a by using the value of the perimeter of one of its faces. The volume of the cube will be given as , that is, the cube of the length of its side.
Complete step-by-step answer:
In geometry, a cube is a three dimensional solid object bounded by six square faces. At each vertex of the cube, three sides meet.
We know that each of the forces of a cube is a square and the perimeter of a square is given as:
Since, we have assumed here that the length of one side of the cube is ‘a’ units. Therefore, the perimeter of one face of the cube is = 4a.
Also, it is given that the perimeter is = 24 cm.
So, we can write:
So, the length of each of the sides of the cube is equal to 6 cm.
Now, we know that the volume of a cube is given as:
We have already found that the length of the side of the cube is 6 cm. Therefore, the volume of the cube will be:
Hence, the volume of the given cube is .
Note: Students should note here that each of the faces of a cube is in the form of a square and hence we can use the formula of perimeter of a square to find the length of each side of the given cube. Students should also remember the correct formula for the volume of a cube to avoid mistakes.
Complete step-by-step answer:

In geometry, a cube is a three dimensional solid object bounded by six square faces. At each vertex of the cube, three sides meet.
We know that each of the forces of a cube is a square and the perimeter of a square is given as:
Since, we have assumed here that the length of one side of the cube is ‘a’ units. Therefore, the perimeter of one face of the cube is = 4a.
Also, it is given that the perimeter is = 24 cm.
So, we can write:
So, the length of each of the sides of the cube is equal to 6 cm.
Now, we know that the volume of a cube is given as:
We have already found that the length of the side of the cube is 6 cm. Therefore, the volume of the cube will be:
Hence, the volume of the given cube is
Note: Students should note here that each of the faces of a cube is in the form of a square and hence we can use the formula of perimeter of a square to find the length of each side of the given cube. Students should also remember the correct formula for the volume of a cube to avoid mistakes.
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