Question

Each face of a cube has a perimeter equal to 32cm. Find its surface area.

Answer 1

Hint: In this question, we are given the perimeter of the face of a cube. We need to find the surface area of the cube. All faces of a cube are in the shape of squares. So, we will use the perimeter of the square to find the side of the square which will be the edge of the cube.
Using the edge of the cube, we will find the surface area of the cube. Surface area of a cube with side 'a' is equal to $6{{a}^{2}}$. Perimeter of a square with side 'a' is equal to 4a.

Complete step by step answer:
Here, we are given a cube whose face has a perimeter equal to 32cm. A cube is a three dimensional shape made of 6 square faces.

Since every face of a cube is a square, therefore we are given the perimeter of a square.
Let us suppose that, the side of the square is s then it will also be the edge of the cube.
Now, the perimeter of the square with side s is given by 4s. So we can say that, $4s=32cm$.
Dividing both sides by 4 we get, $s=\dfrac{32}{4}cm=8cm$.
Hence, the edge of the cube is 8cm.
Now let us find the surface area of the cube. We know that the surface area of a cube with side s is given by $6{{s}^{2}}$.
So the surface area of given cube with side 8cm will be equal to $6{{\left( 8cm \right)}^{2}}\Rightarrow 6\times 8\times 8c{{m}^{2}}\Rightarrow 384c{{m}^{2}}$.

Hence the required surface area of the cube is $384c{{m}^{2}}$.

Note: Students should not forget to write units after finding measurements. Squared units are used for areas. Since the perimeter and length were in centimeters so area is found in squared centimeters.