# Solid Geometry

## Cube

A cube is a three-dimensional figure with six matching square sides.
The dotted lines indicate edges hidden from your view. Volume

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 s2.
Since a cube has six square-shape sides, its total surface area is 6 times s2.
Inverse formula:
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For example:
The length of the cube’s side is 3.8 cm.
Volume = S3 (Substitute the length in formula)
= 3.83 (Multiply the length three times)
= 3.8 · 3.8 · 3.8 = 54.87 cm3
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 = S3 (Substitute the length of box in formula)
= 213 (Expand the value in three)
= 21 · 21 · 21 (Multiply the value 21 three times)
= 9261 cm3
For example:
The side of a cube is 5cm. Find its total surface area.
Total surface area = 6a2, where a is side.
Given that a = 5cm.
Total surface area of the cube = 6 · 52
= 6 · 25
= 150 cm2.
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 = 6s2
= 6(3)2
= 54 cm2

### 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 cm3. 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

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