Transcript Slide 1

10-3 Volume of Pyramids & Cones
Warm Up
Problem of the Day
Lesson Presentation
Course 2
10-3 Volume of Pyramids and Cones
Learn to find the 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.
Course 2
10-3 Volume of Pyramids and Cones
In fact, the volume of a pyramid is exactly onethird 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.
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.
4 ft
V=
1
Bh
3
B = 5 · 7 = 35
V = 1 · 35 · 4
3
5 ft
V ≈ 46.7 ft3
Use the formula.
Find the area of the
rectangular base.
Substitute for B and h.
Multiply.
Round the measurements.
The answer is reasonable.
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.
4 ft
V=
1
Bh
3
B = 8 · 7 = 56
8 ft
Course 2
V = 1 · 56 · 4
3
V ≈ 74.7 ft3
Use the formula.
Find the area of the
rectangular base.
Substitute for B and h.
Multiply.
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.
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
V = 3 Bh
1
V  3 · 78.5 · 6
V  157 yd3
Course 2
Use the formula.
The base is a circle so
B =  · r2  3.14 · 52  78.5.
Substitute for B and h.
Multiply.
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.
7 cm
3 cm
1
V = 3 Bh
Use the formula.
The base is a circle so
B =  · r2  3.14 · 32 
1
28.26.
V  3 · 28.26 · 7 Substitute for B and h.
V  65.9 cm3
Course 2
Multiply.
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 .
1
V = 3 Bh
3 yd
1
V  3 · 12.56 · 3
2 yd
Course 2
V = 12.6 yd3
Use the formula.
The base is a circle so
B =  · r2  3.14 · 32  12.56.
Substitute for B and h.
Multiply.
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.
1
V  3 · 12.56 · 7
Use the formula.
The base is a circle so B =
4 2
2
 · r  3.14 ·
 12.56.
2
Substitute for B and h.
V  29.3 cm3
Multiply.
1 ·  22 · 7
V≈
3
1 ·  ≈ 1.
3
1
V = 3 Bh
7 cm
4 cm
Estimate
 28 cm3
Course 2
The answer is reasonable.
10-3 Volume of Pyramids and Cones
Lesson Quiz
Find the volume of each pyramid or cone to
the nearest tenth. Use 3.14 for . Estimate to
check whether the answer is reasonable.
1.
2.
80 ft3
301.4 yd3
3.
Course 2
252 ft3