# Solid Geometry

## Three-dimensional shapes

## Cube

A cube is a three-dimensional figure with six matching square sides.

The dotted lines indicate edges hidden from your view.

If

*s*is the length of one of its sides, then the volume of the cube is*s*·*s*·*s*### Surface area

The area of each side of a cube is s

^{2}.Since a cube has six square-shape sides, its total surface area is 6 times s

^{2}.Inverse formula:

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*s=**TSA**6*<![endif]–>**For example:**

The length of the cube’s side is 3.8 cm.

Volume = S

^{3}(Substitute the length in formula)= 3.8

^{3}(Multiply the length three times)= 3.8 · 3.8 · 3.8 = 54.87 cm

^{3}**For example:**

A cube shape box is filled with small balls and the length of box is 21 cm. What is the volume of cube box?

Volume = S

= 213 (Expand the value in three)

^{3}(Substitute the length of box in formula)= 213 (Expand the value in three)

= 21 · 21 · 21 (Multiply the value 21 three times)

= 9261 cm

^{3}**For example:**

The side of a cube is 5cm. Find its total surface area.

Total surface area = 6a

^{2}, where a is side.Given that a = 5cm.

Total surface area of the cube = 6 · 5

^{2}= 6 · 25

= 150 cm

^{2}.**For example:**

Find the surface area of a cube with a side of length 3 cm.

Given that s = 3

Surface area of a cube = 6s

^{2}= 6(3)

^{2}= 54 cm

^{2}### Exercises

1. Find the volume and the total surface area of a cube with sides 8 cm.

2. If the side of a cube is 3.5 inches, find its volume and its total surface area.

3. What is the volume and the total surface area of a cubical box with sides 7 inches?

4. Find the volume and the total surface area of a cube with sides 1.7 feet.

5. Dimensions of a cube: Length = Width = Height = 5.6 inches. Find the volume and the total surface area of the cube.

6. A cube has the side 18 cm long. Calculate the volume and total surface area of the cube.

7. A cube has the side 25cm long . Calculate the volume and the total surface area.

8. The total surface area of a cube is 9126 cm ². Calculate the side.

9. The volume of a cube is 3375 cm

^{3}. Calculate the total surface area of the cube.10. The perimeter of one side of a cube is 120 cm. Calculate the volume and total surface area of the cube. Solution