geometry section 12-5
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Section 12-5Volumes of Pyramids and Cones
Essential Questions
• How do you find volumes of pyramids?
• How do you find volumes of cones?
Volume of a Pyramid
Volume of a Pyramid
V = 13Bh
Volume of a Pyramid
B = area of the base
V = 13Bh
Volume of a Pyramid
B = area of the baseh = height of the pyramid
V = 13Bh
Example 1Find the volume of the pyramid.
Example 1Find the volume of the pyramid.
V = 13Bh
Example 1Find the volume of the pyramid.
V = 13Bh
B = area of the square base
Example 1Find the volume of the pyramid.
V = 13Bh
B = area of the square base
V = 13 (3)2(7)
Example 1Find the volume of the pyramid.
V = 13Bh
B = area of the square base
V = 13 (3)2(7)
V = 21 in3
Volume of a Cone
Volume of a Cone
V = 13Bh or V = 1
3 πr 2h
Volume of a Cone
V = 13Bh or V = 1
3 πr 2h
B = area of the base: B = πr 2
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
Example 2Find the volume of the cone to the nearest hundredth.
Example 2Find the volume of the cone to the nearest hundredth.
V = 13 πr 2h
Example 2Find the volume of the cone to the nearest hundredth.
V = 13 πr 2h
V = 13 π(5)2(12)
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
Example 3Find the volume of the cone to the nearest hundredth.
Example 3Find the volume of the cone to the nearest hundredth.
V = 13 πr 2h
Example 3Find the volume of the cone to the nearest hundredth.
V = 13 πr 2h
V = 13 π(3.5)2(13)
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
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?
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
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)
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
Problem Set
Problem Set
p. 860 #1-12, 17, 18 all; skip #2, 6
“From a small seed a mighty trunk may grow.” - Aeschylus
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