## Cuboid

A rectangular solid is also called a rectangular prism or cuboid.

The volume is found using the formula:

Inverse formulas:

### Surface area

The total surface area (TSA) of a cuboid is the sum of the areas of its six faces.

That is:

#### For example:

Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm.

TSA = 2 (lw+wh+hl)

TSA = 2 (8⋅6+6⋅5+5⋅8) = 2(48+30+40) = 236 cm

^{2}So, the total surface area of this cuboid is 236 cm

^{2}^{ }

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#### For example:

We want to find the volume of this cuboid in cm

^{3}To find the volume we mulptiply the sides.

V=3∙4∙7 = 84 cm^{3}

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^{Exercises}

- A cuboid has lateral surface 199 cm
^{2 }. The base has sides 23 cm and 14 cm long. Calculate the height. Solution - A cuboid has its height equal to the diagonal of the base. The sum of the two sides of the base is 21 cm and one is 3/4 of the other. Calculate the total surface area.
- The diagonal of a cuboid is 117 cm the base has sides 36 cm and 27 cm long. Calculate the volume and the total surface area.
- A cuboid has the perimeter of the base equal to 84 dm and one side is 3/4 of the other. The height is 40 dm long. Calculate the total surface area.
- The sum of two sides of a cuboid is 14 cm and one side is 4/3 of the other. Knowing that the total surface area is 768 cm
^{2 }, calculate the third dimension of the cuboid. - The difference between two sides of a cuboid is 14 cm and one side 15/8 of the other. The third side (height) is 33 cm long. A second cuboid has a squared base with 121 cm
^{2 }area and has the same lateral area of the first one. Calculate the third side. - A cuboid has two sides 13 cm and 15 cm long. The total surface area is 950 cm
^{2 }. Calculate the volume. Solution - The squared base of a cuboid is 576 cm
^{2 }. The height of the cuboid is 1/12 of the perimeter of the base. Calculate lateral surface and volume. - The volume of a cuboid is 108 cm
^{3}^{ }and two sides are 4.5 cm and 6 cm long. Calculate the diagonal and the total surface area of the cuboid. - The volume of a cuboid is 1768 cm
^{3}^{ }. The sum and the difference between two sides are 30 cm and 4 cm. Calculate the lenght of the third side. - The perimeter of the base of a cuboid is 66 cm and one side is 6/5 of the other. The volume is 2.97dm
^{3}^{ }. Calculate the lenght of the third side.

its fun doing when i have time…

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