Volume Ratios of Similar Solids Lesson 99 Volume Ratios of Similar Solids

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

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 3 2 3 1 8 What are some other ways to write this ratio? 1:8 1 to 8

The Solids are similar. Find the ratio of larger volume to the smaller volume 6 4 = 3 2 𝑎 3 𝑏 3 = 3 3 2 3 27 8 What is the ratio of the corresponding sides of corresponding faces?

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 3 2 3 3 3 = 𝑉 2058𝜋 𝑉= 2 3 ∙2058𝜋÷ 3 3 𝑉≈1916 𝑓𝑡 3

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