1. 12.5: Volumes of Pyramids and Cones
Objective:
Use the formula for volume of pyramids and cones to solve problems

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

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. 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

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

11. 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