12.5: Volumes of Pyramids and Cones Objective: Use the formula for volume of pyramids and cones to solve problems

Vocab Volume of a Pyramid 𝑉= 1 3 𝐵ℎ B = area of base h = height of pyramid 𝑉= 1 3 𝐵ℎ

Example 1 𝑉= 1 3 𝐵ℎ 𝐵=3∗3=9 ℎ=7 𝑉=9∗7=63 𝑖𝑛 3 Find the volume of the square pyramid. Label the units. 𝑉= 1 3 𝐵ℎ 𝐵=3∗3=9 ℎ=7 𝑉=9∗7=63 𝑖𝑛 3

Example 2 𝑉= 1 3 𝐵ℎ 𝐵= 𝑏∗ℎ 2 = 5∗9 2 =22.5 ℎ=10 𝑉=22.5∗10=225 𝑖𝑛 3 Find the volume of the triangular pyramid. Label the units. 𝑉= 1 3 𝐵ℎ 𝐵= 𝑏∗ℎ 2 = 5∗9 2 =22.5 ℎ=10 𝑉=22.5∗10=225 𝑖𝑛 3

You Try Find the volume of the pentagonal pyramid. Label the units. Do on your own first!

You Try 𝑉= 1 3 𝐵ℎ 𝐵= 1 2 𝑎𝑃= 1 2 ∗3∗22=33 ℎ=12 𝑉=33∗12=396 𝑐𝑚 3 Find the volume of the pentagonal pyramid. Label the units. 𝑉= 1 3 𝐵ℎ 𝐵= 1 2 𝑎𝑃= 1 2 ∗3∗22=33 ℎ=12 𝑉=33∗12=396 𝑐𝑚 3

Vocab Volume of a Cone 𝑉= 1 3 π 𝑟 2 ℎ r = radius of base h = height of cone 𝑉= 1 3 π 𝑟 2 ℎ

Example 3 𝑉= 1 3 π 𝑟 2 ℎ 𝑟=5 ℎ=12 𝑉= 1 3 π (5) 2 ∗12=100π 𝑖𝑛 3 Find the volume of the cone. Leave your answers in terms of π and label the units. 𝑉= 1 3 π 𝑟 2 ℎ 𝑟=5 ℎ=12 𝑉= 1 3 π (5) 2 ∗12=100π 𝑖𝑛 3

Example 4 𝑉= 1 3 π 𝑟 2 ℎ 𝑟=9.1 ℎ=25 𝑉= 1 3 π (9.1) 2 ∗25=2168 𝑓𝑡 3 Find the volume of the oblique cone. Round your answer to the tenth. 𝑉= 1 3 π 𝑟 2 ℎ 𝑟=9.1 ℎ=25 𝑉= 1 3 π (9.1) 2 ∗25=2168 𝑓𝑡 3

You Try Find the volume of each cone. Do on your own first!

You Try 𝑉= 1 3 π 𝑟 2 ℎ 𝑟=3.5 ℎ=4 𝑉= 1 3 π (3.5) 2 ∗4=51.3 𝑖𝑛 3 Find the volume of each cone. 𝑉= 1 3 π 𝑟 2 ℎ 𝑟=3.5 ℎ=4 𝑉= 1 3 π (3.5) 2 ∗4=51.3 𝑖𝑛 3