geometry section 12-5

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Section 12-5 Volumes of Pyramids and Cones

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Page 1: Geometry Section 12-5

Section 12-5Volumes of Pyramids and Cones

Page 2: Geometry Section 12-5

Essential Questions

• How do you find volumes of pyramids?

• How do you find volumes of cones?

Page 3: Geometry Section 12-5

Volume of a Pyramid

Page 4: Geometry Section 12-5

Volume of a Pyramid

V = 13Bh

Page 5: Geometry Section 12-5

Volume of a Pyramid

B = area of the base

V = 13Bh

Page 6: Geometry Section 12-5

Volume of a Pyramid

B = area of the baseh = height of the pyramid

V = 13Bh

Page 7: Geometry Section 12-5

Example 1Find the volume of the pyramid.

Page 8: Geometry Section 12-5

Example 1Find the volume of the pyramid.

V = 13Bh

Page 9: Geometry Section 12-5

Example 1Find the volume of the pyramid.

V = 13Bh

B = area of the square base

Page 10: Geometry Section 12-5

Example 1Find the volume of the pyramid.

V = 13Bh

B = area of the square base

V = 13 (3)2(7)

Page 11: Geometry Section 12-5

Example 1Find the volume of the pyramid.

V = 13Bh

B = area of the square base

V = 13 (3)2(7)

V = 21 in3

Page 12: Geometry Section 12-5

Volume of a Cone

Page 13: Geometry Section 12-5

Volume of a Cone

V = 13Bh or V = 1

3 πr 2h

Page 14: Geometry Section 12-5

Volume of a Cone

V = 13Bh or V = 1

3 πr 2h

B = area of the base: B = πr 2

Page 15: Geometry Section 12-5

Volume of a Cone

h = height of the cone

V = 13Bh or V = 1

3 πr 2h

B = area of the base: B = πr 2

Page 16: Geometry Section 12-5

Example 2Find the volume of the cone to the nearest hundredth.

Page 17: Geometry Section 12-5

Example 2Find the volume of the cone to the nearest hundredth.

V = 13 πr 2h

Page 18: Geometry Section 12-5

Example 2Find the volume of the cone to the nearest hundredth.

V = 13 πr 2h

V = 13 π(5)2(12)

Page 19: Geometry Section 12-5

Example 2Find the volume of the cone to the nearest hundredth.

V = 13 πr 2h

V = 13 π(5)2(12)

V ≈ 314.16 cm3

Page 20: Geometry Section 12-5

Example 3Find the volume of the cone to the nearest hundredth.

Page 21: Geometry Section 12-5

Example 3Find the volume of the cone to the nearest hundredth.

V = 13 πr 2h

Page 22: Geometry Section 12-5

Example 3Find the volume of the cone to the nearest hundredth.

V = 13 πr 2h

V = 13 π(3.5)2(13)

Page 23: Geometry Section 12-5

Example 3Find the volume of the cone to the nearest hundredth.

V = 13 πr 2h

V = 13 π(3.5)2(13)

V ≈166.77 ft3

Page 24: Geometry Section 12-5

Example 4At the top of a stone tower is a pyramidion in the shape of a

square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of

the pyramidion rounded to the nearest hundredth?

Page 25: Geometry Section 12-5

Example 4At the top of a stone tower is a pyramidion in the shape of a

square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of

the pyramidion rounded to the nearest hundredth?

V = 13Bh

Page 26: Geometry Section 12-5

Example 4At the top of a stone tower is a pyramidion in the shape of a

square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of

the pyramidion rounded to the nearest hundredth?

V = 13Bh

V = 13 (36)2(52.5)

Page 27: Geometry Section 12-5

Example 4At the top of a stone tower is a pyramidion in the shape of a

square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of

the pyramidion rounded to the nearest hundredth?

V = 13Bh

V = 13 (36)2(52.5)

V = 22680 cm3

Page 28: Geometry Section 12-5

Problem Set

Page 29: Geometry Section 12-5

Problem Set

p. 860 #1-12, 17, 18 all; skip #2, 6

“From a small seed a mighty trunk may grow.” - Aeschylus