1. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
Learn to find the volume of pyramids and cones.

2. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
Suppose you have a square-pyramid-shaped container and a square-prism-shaped container, and the bases and heights are the same size. If you pour sand from the pyramid into the prism, it appears that the prism holds three times as much sand as the pyramid.

3. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
In fact, the volume of a pyramid is exactly one-third the volume of a prism if they have the same height and same-size base The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex.

4. Additional Example 1: Finding the Volume of a Rectangular Pyramid
Course 2
10-3
Volume of Pyramids and Cones
Additional Example 1: Finding the Volume of a Rectangular Pyramid
Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3
V = Bh
Use the formula.
4 ft
Find the area of the
rectangular base.
B = 5 · 7 = 35 1 3
V =
· 35 · 4
Substitute for B and h.
7 ft
5 ft
V ≈ 46.7 ft3
Multiply. 1 3
Estimate
V =
· 30 · 5
Round the measurements.
V = 50 ft3
The answer is reasonable.

5. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
Check It Out: Example 1
Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3
V = Bh
4 ft
Use the formula.
Find the area of the
rectangular base.
B = 8 · 7 = 56 1 3
V =
· 56 · 4
Substitute for B and h.
7 ft
8 ft
V ≈ 74.7 ft3
Multiply. 1 3
Estimate
V =
· 60 · 4
Round the measurements.
V = 80 ft3
The answer is reasonable.

6. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base. The height of a cone is the perpendicular distance from the cone’s base to its vertex.

7. Additional Example 2A: Finding the Volume of a Cone
Course 2
10-3
Volume of Pyramids and Cones
Additional Example 2A: Finding the Volume of a Cone
Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3
Use the formula.
The base is a circle so
B =  · r2  3.14 · 52  78.5.
V = Bh 1 3
V 
· 78.5 · 6
Substitute for B and h.
V  157 yd3
Multiply.
·  ≈ 1. 1 3
V ≈
·  52 · 6 1 3
Estimate
 150 yd3
The answer is reasonable.

8. Additional Example 2B: Finding the Volume of a Cone
Course 2
10-3
Volume of Pyramids and Cones
Additional Example 2B: Finding the Volume of a Cone
Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3
Use the formula.
The base is a circle so
B =  · r2  3.14 · 32 
V = Bh
7 cm
3 cm 1 3
V 
· · 7
Substitute for B and h.
V  65.9 cm3
Multiply.
·  ≈ 1. 1 3
V ≈
·  32 · 7 1 3
Estimate
 63 cm3
The answer is reasonable.

9. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
Check It Out: Example 2A
Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3
Use the formula.
The base is a circle so
B =  · r2  3.14 · 32 
V = Bh
3 yd
2 yd 1 3
V 
· · 3
Substitute for B and h.
V = yd3
Multiply.
·  ≈ 1. 1 3
V ≈
·  22 · 3 1 3
Estimate
 12 yd3
The answer is reasonable.

10. Volume of Pyramids and Cones
Course 2
10-3
Volume of Pyramids and Cones
Check It Out: Example 2B
Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.
Use the formula.
The base is a circle so B =
 · r2  3.14 · 
4 2 1 3
V = Bh
7 cm
4 cm 1 3
V 
· · 7
Substitute for B and h.
V  29.3 cm3
Multiply.
·  ≈ 1. 1 3
V ≈
·  22 · 7 1 3
Estimate
 28 cm3
The answer is reasonable.