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We already know that if two shapes are similar their corresponding sides are in the same ratio, and their corresponding angles are equal.

Look at the two cubes below:

The cubes are similar, and the ratio of their lengths is a:b or

- Question
What is the ratio of:

- the area of their faces?
- their volumes?

- Answer
- Cube 'a' has a face area of a
^{2}Cube 'b' has a face area of b

^{2}The ratio of their areas is a

^{2}:b^{2}or - Cube 'a' has a volume of
a
^{3}Cube 'b' has a volume of b

^{3}The ratio of their volumes is a

^{3}:b^{3}or

- Cube 'a' has a face area of a

For any pair of similar shapes, the following is true:

**Ratio of lengths = a:b or **

Ratio of areas = a^{2}:b^{2} or

Ratio of volumes = a^{3}:b^{3} or

- Question
These two shapes are similar. What is the length of

**x**?

- Answer
The ratio of the areas is 25:36 (a

^{2}:b^{2})The ratio of the lengths is a:b Therefore, we find the square roots of 25 and 36. Ratio of lengths = 5:6

5:6 = 2:x

So

(multiply both sides by 2) = x

**x = 2.4cm**

Now you try one.

- Question
Two similar pyramids have volumes of 64cm

^{3}and 343cm^{3}. What is the ratio of their surface areas?

- Answer
The answer is

**16:49**. Here is how to work it out. Try to fill in the blanks below:Ratio of volumes = 64:?

To find the ratio of the lengths, we find the cube roots of 64 and ?

Therefore, the ratio of the lengths is ?:7

To find the ratio of the areas, we square ? and 7

The ratio of the areas is 16:49.

**Now try a **Test Bite

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