## How to Find Volume and Surface Area of Cubes

### What Does Surface Area of Cube Mean?

The total area of all the faces outside a cube is called the surface area. The important word in this definition is "outside" because the surface area is the number of square units it would take to cover the figure's outside.
Always use square units to talk about surface area.
Since the cube's surface is in the shape of a square. So, the square of the edge is equal to the area of each face of the cube.

Let $$a$$ be the length of a cube's edge. So, the area of one face is equal to $$a^2$$ (Using the formula for the square area)
There are six faces in all. Therefore,

The TSA for a cube is $$a^2 \ + \ a^2 \ + \ a^2 \ + \ a^2 \ + \ a^2 \ + \ a^2$$ $$⇒$$ TSA $$= \ 6a^2$$

### How to Find the Surface Area of Cubes

Now that you know the formula for finding the surface area of a cube, you can use the three steps below to solve the practice problems:

• Step 1: Find the value of $$a$$, which is the cube's edge length.
• Step 2: Use that number in the formula for the surface area of a cube.
• Step 3: Solve the problem and write the answer in square units.

### Example:

Figure out how much it will cost to paint a cube-shaped aquarium with sides that are $$5.2$$ m long. If it costs INR $$7/m^2$$ to paint an aquarium,

The total area of the aquarium's surface $$= \ 6$$ (side)$$^2 \ = \ 6(5.2)^2 \ = \ 162.24$$ m$$^2$$

The overall cost of painting the aquarium is $$7 \times 162.24 \ = \ Rs. \ 1135.68$$

### Exercises for Volume and Surface Area of Cubes

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1) $$\color{red}{486}$$ in$$^2$$
2) $$\color{red}{1536}$$ mm$$^2$$
3) $$\color{red}{1734}$$ cm$$^2$$
4) $$\color{red}{600}$$ m$$^2$$
5) $$\color{red}{54}$$ in$$^2$$
6) $$\color{red}{1944}$$ in$$^2$$
7) $$\color{red}{726}$$ mm$$^2$$
8) $$\color{red}{96}$$ in$$^2$$
9) $$\color{red}{864}$$ cm$$^2$$
10) $$\color{red}{2166}$$ in$$^2$$

## Volume and Surface Area of Cubes Practice Quiz

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