# Cuboid Rectangular Prism

**Definition of a cuboid rectangular prism:** A cuboid is a solid with six rectangular faces, the opposite faces being equal in size.

In other words a cuboid rectangular prism is a box-shaped object. It has six sides, all of its faces are rectangles and the angles are right angles.

It is also a prism because the cross-section is the same through out the the shape. It is called a rectangular prism.

**Cuboids in the real world**

Cuboids are absolutely everywhere. The room you are sitting in is probably a cuboid. Alot of everyday objects are cuboids. Cuboids are just boxes.

Here is a picture of my match box..Lo an behold, Its a cuboid.

Another cuboid, for my nasty cough the medicine bottle sits in this lovely cuboid.

Then there is this red cuboid where all my junk sits in under the table, which just happens to be cuboid(ish) also.

**How to find the Volume and Surface Area of a Cuboid**

** Volume**

To find the volume of a cuboid we multiply the sides of the length, width and height. The formula for this would look like this:

Volume = Height × Width × Length

It is usually shortened to using the first letters of each word, such as:

V = H × W × L

To make it even more shorter we can take out the multiplication sign and put the letters next to each other:

V= HWL

**Example: Find the volume of the cuboid with dimensions 3cm, 2cm and 10cm**

So, the basic rule of finding the volume of a cuboid is to multiply the length by the width by the height.

In this example, the length, width and height is 3cm, 2cm and 10cm.

Volume = 3 × 2 × 10=60

Volume for this cuboid would be 60cm³ (The little 3 on the top is pronounced as 'cube', ³.

This is because we are multiplying the cm three times, or rather multiplying 3 lots of numbers).

**Surface Area**

The surface area is found by using this formula

Surface Area = 2wl + 2lh + 2hw

(Note: 2wl means 2×width×length, 2lh means 2×length×height and so on)

**Example: Find the volume of the cuboid with dimensions 3cm, 2cm and 10cm**

We have taken the same cuboid dimensions as the above example. This time we are working out its surface area.

Lets start with wl, this is the width×length. Which is the yellow part of the box. Its width is 2cm and its length is 10cm.

2×10=20.

Since we also have the bottom part of the cuboid to consider, we multiply this number 20 by 2 to give 40.

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Next is lh, length×height. Which is the the light blue side of the cuboid. The length is 10cm and the height is 3cm.

10 ×3=30.

Multiply this 30 by 2 because we also have the opposite side of the cuboid to add to.

30×2=60.

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Finally, we have height ×width, which is the pink side of the cuboid.

3×2=6.

Then multiply this number by 2 to include the opposite side of the cuboid to give 12.

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Add these numbers together to give:

40+60+12=112cm² ...This is the final answer, PHEW, got there in the end!

(Note it is cm², since we are finding out the area it is cm×cm)

I understand that this is very long winded and tedious, but if you just take a step back and think about what you are trying to work out (the area all round the box), its not that difficult at all.

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