# Similar solids

##### Intros

###### Lessons

##### Examples

###### Lessons

**Identify Similar Solids**Which of the following are similar solids?

**Proof of the Relationships Between Scale Factor, Area Ratio and Volume Ratio**Use the following similar solids to prove the relationships between the scale factor, surface area ratio and volume ratio.

**Given the Scale Factors, Find a Surface Area**Given two similar hemispheres. The radius of the smaller hemisphere is $5m$ and that of the larger hemisphere is $7m$. If the surface area of the larger hemisphere is $147m^{2}$, what is the surface area of the smaller hemisphere?

**Given the Volumes, Find the Scale Factors**Given that the volumes of the two similar prisms are $729cm^{3}$ and $1331cm^{3}$ respectively. What is the scale factor of the smaller prism to the larger prism?

**Scale Factors Doubled, Find a Volume**The dimensions of a pyramid figure with a volume of $24m^{3}$ have been doubled. What is the volume of the new pyramid figure?

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###### Topic Notes

In this lesson, we will learn:

- Identify Similar Solids
- Proof of the Relationships Between Scale Factor, Area Ratio and Volume Ratio
- Given the Scale Factors, Find a Surface Area
- Given the Volumes, Find the Scale Factors
- Scale Factors Doubled, Find a Volume

- Solid: A three-dimensional object
- Two solids are similar when the ratios of their corresponding measures are constant.
- Scale factor:
- The ratios of the corresponding measures of two objects.
- A numeric multiplier used for scaling.

- If two similar solids have a scale factor of $\frac{a}{b}$, then
- They have a surface area ratio of $(\frac{a}{b})^{2}$.
- They have a volume ratio of $(\frac{a}{b})^{3}$.

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