Question

The perimeter of one face of a cube is $40cm$ . The volume of the cube (in $c{{m}^{3}}$ ) is:

Answer 1

Hint: All the faces of a cube are a square. Therefore we are given the perimeter of a square. The length of all sides of a square are the same so the formula for writing perimeter of a square is given by $P=4\cdot a$ where P= perimeter and a= length of side of the square. We can use this to find the side of the square and since all the edges of a cube are equal therefore we have a side of the cube. Volume of a cube is given by $V={{a}^{3}}$ where a= length of side of a cube.

Complete step-by-step answer:
Since, all the faces of a cube are squares therefore we have 40cm as the perimeter of a square so we can write $P=4a=40cm$ from this we can find the length of the side.
$4a=40cm$

Dividing both sides with 4 we have,
$a=10cm$

This is the side of the square. Since, all the edges of a cube are equal therefore ‘a’ is the side of the cube.

Now, volume of a cube is given by: $V={{a}^{3}}$

Substituting the value of a we have,
$V={{(10cm)}^{3}}={{10}^{3}}c{{m}^{3}}=1000c{{m}^{3}}$

Therefore, the volume of the cube is $1000c{{m}^{3}}$ .

Hence, the answer is $1000c{{m}^{3}}$ .

Note: If we were given the perimeter of a cuboid then this much information would not have been sufficient to find volume of a cuboid. Cuboid has three variables length, breadth and height. Its volume is given by $V=lbh$ . Cube is a special case of cuboid when all the three variables become equal means $l=b=h$ . Hence, the volume of cube is given by $V={{a}^{3}}$ where a is its side length.