1. Volume Ratios of Similar Solids
Lesson 99
Volume Ratios of Similar Solids

2. Two similar solids with a scale factor 𝑎:𝑏 then:
Theorem 99-1
Two similar solids with a scale factor 𝑎:𝑏 then:
Perimeter of corresponding faces is 𝑎:𝑏 or 𝑎 𝑏
Area of corresponding faces is 𝑎 2 : 𝑏 2 or 𝑎 2 𝑏 2
Volume is 𝑎 3 : 𝑏 3 or 𝑎 3 𝑏 3

3. Find the volume ratio of figure b to figure A
Fig. A surface area is 20 units squared Fig. B surface area is 5 units squared
𝑏 2 𝑎 2 = 5 20
𝑏 𝑎 = 1 2
𝑏 3 𝑎 3 =
1 8
What are some other ways to write this ratio?
1:8
1 to 8

4. The Solids are similar. Find the ratio of larger volume to the smaller volume
6 4 = 3 2 𝑎 3 𝑏 3 =
What is the ratio of the corresponding sides of corresponding faces?

5. Application in farming
A scale model of a silo in the shape of a cylinder has a radius of 7 inches & a height of 42 inches. Determine the volume of the actual silo, which will be scaled up by a factor of 8, to the nearest cubic foot.
Factor of 8:1 is in feet. 8𝑓𝑡 1𝑓𝑡 = 8𝑓𝑡 12𝑖𝑛 = 2𝑓𝑡 3𝑖𝑛 𝑉=𝜋 𝑟 2 ℎ 𝑉=𝜋 7 2 ∙42 𝑉=2058𝜋 𝑖𝑛 = 𝑉 2058𝜋 𝑉= 2 3 ∙2058𝜋÷ 3 3 𝑉≈1916 𝑓𝑡 3

6. Two similar solids with a scale factor 𝑎:𝑏 then:
Questions?
Two similar solids with a scale factor 𝑎:𝑏 then:
Perimeter 𝑎:𝑏 or 𝑎 𝑏
Area 𝑎 2 : 𝑏 2 or 𝑎 2 𝑏 2
Volume 𝑎 3 : 𝑏 3 or 𝑎 3 𝑏 3