10-3 volume of pyramids & cones course 2 warm up warm up problem of the day problem of the day...

10-3 Volume of Pyramids & Cones

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpFind each volume to the nearest tenth. Use 3.14 for .

1. cylinder: radius = 6 m, height = 11 m

1,243.4 m3

1,114.6 cm3

612 ft3

Course 2

10-3 Volume of Pyramids and Cones

904.3 m3

2. rectangular prism: length = 10 cm, width = 8.64 cm, height = 12.9 cm

3. triangular prism: base area = 34 ft2, height = 18 ft

4. cylinder: diameter = 8 m, height = 18 m

Problem of the DayWhen my age is divided by 2, 3, 4, or 6 there is always a remainder of 1, but when it is divided by 7 there is no remainder. How old am I?49

Course 2


Learn to find the volume of pyramids and cones.

Course 2


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


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.

Course 2


Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Additional Example 1: Finding the Volume of a Rectangular Pyramid

V = 13

Bh Use the formula.

B = 5 · 7 = 35Find the area of the rectangular base.

V = 13

· 35 · 4 Substitute for B and h.

V ≈ 46.7 ft3

Estimate

5 ft 7 ft

4 ft

Multiply.

V = 13

· 30 · 5 Round the measurements.

V = 50 ft3 The answer is reasonable.Course 2


Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Check It Out: Example 1

V = 13

Bh Use the formula.

B = 8 · 7 = 56Find the area of the rectangular base.

V = 13

· 56 · 4 Substitute for B and h.

V ≈ 74.7 ft3

Estimate

Multiply.

V = 13

· 60 · 4 Round the measurements.

V = 80 ft3 The answer is reasonable.Course 2


8 ft 7 ft

4 ft

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


Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.

Additional Example 2A: Finding the Volume of a Cone

V =13 Bh

V 13 · 78.5 · 6

V 157 yd3

Estimate

Use the formula. The base is a circle so B = · r2 3.14 · 52 78.5.

Substitute for B and h.

Multiply.

Course 2


13

· ≈ 1.13V ≈ · 52 · 6

150 yd3 The answer is reasonable.


Additional Example 2B: Finding the Volume of a Cone

V =13 Bh

V 13 · 28.26 · 7

V 65.9 cm3

Estimate



Multiply.

Course 2


13

· ≈ 1.13V ≈ · 32 · 7

63 cm3 The answer is reasonable.

7 cm

3 cm


Check It Out: Example 2A

V =13 Bh

V 13 · 12.56 · 3

V = 12.56 yd3

Estimate



Multiply.

Course 2


13

· ≈ 1.13V ≈ · 22 · 3

12 yd3 The answer is reasonable.

3 yd

2 yd


Check It Out: Example 2B

V =13 Bh

V 13 · 12.56 · 7

V 29.3 cm3

Estimate


Multiply.

Course 2


13

· ≈ 1.13V ≈ · 22 · 7

28 cm3 The answer is reasonable.

7 cm

4 cm

Use the formula. The base is a circle so B =

· r2 3.14 · 2 12.56.4 2

Lesson QuizFind the volume of each pyramid or cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.

3.

1. 2.

80 ft3

301.4 yd3

252 ft3

Course 2


10-3 volume of pyramids & cones course 2 warm up warm up problem of the day problem of the day...

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