Similar Solids

Lesson 23

1. Draw and label two circles that are similar. Identify their scale factor.

2. Draw two rectangles that are similar. Identify their scale factor.  

3. ∆ABC is similar to ∆ XYZ. Use a proportion to solve for x.

6

12

4

x

Target:Use ratios and proportions when finding scale factors, linear

ratios, area ratios and volume ratios of similar solids.

Similar Solids: Solids with the same shape and all corresponding dimensions are

proportional.

If two solids are similar then:

Their linear ratio (scale factor) is a : b.

The ratio of their areas is a2 : b2.

The ratio of their volumes is a3 : b3.

Are the cylinders similar?

Find the ratio of the radii.

Find the ratio of the heights then simplify.

Cylinders are similar if their radii and heights have the same ratio.

Cylinder A and B are similar.

2

3

2

3

6

9

Two solids have a scale factor 3 : 4.a. Find their area ratio.

Square the scale factor. 32 : 42 → 9 : 16

b. Find the volume ratio.

Raise the scale factor to the third power. 33 : 43 → 27 :

64

Two children each have an ice cream cone. The ice cream cones are similar in shape, but one is larger than the other. The cones have a scale factor of 2:5. The volume of the small cone is 121.4 cm3. Find the volume of the larger cone.

Find the volume ratio. a3 : b3 → 23 : 53 → 8 : 125 → Write a proportion using the volume ratio. Set the cross products equal. 8x = 15175 Divide both sides by 8. 8 8 The volume of the cone is 1,896.875 cm3.

x

4.121

125

8

125

8

1. Two similar solids have an area ratio of 4² : 9².

a) Identify the ratio of the linear measures.

b) Identify the ratio of the volumes.

c) What is the scale factor between the solids?

2. Two cylinders have a scale factor of 2 : 7. The surface area of the large cylinder is 595 square inches. Find the surface area of the smaller cylinder. Round to the nearest hundredth.

Jeremy was told the scale factor between two solids was 4 : 7. What additional conclusions can Jeremy make about the solids?

When and where is volume used in daily life?