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04/14/11 Volume #16
Today’s Plan:-Warm-up & Correct Homework-Volume-Assignment
Warm-Up
LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.
LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.
Start working on the volume side of the pink worksheet. Show your formula, substitution, and answer for each problem.
04/14/11 Volume #16
Today’s Plan:-Warm-up & Correct Homework-Volume-Assignment
Problem Solving Page
LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.
04/14/11 Volume #16
Today’s Plan:-Warm-up & Correct Homework-Volume-Assignment
Predict:
1.Looking at a pyramid and prism that share the same size base and height, how much smaller is the pyramid’s volume?
2. Looking at a cone and cylinder that share the same size base and height, how much smaller is the cone’s volume?
LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.
If you pour sand from a pyramid-shaped container into a prism-shaped container with the same height, base shape, and base size, you will discover an interesting relationship. The prism-shaped container holds three times as much sand as the pyramid-shaped container.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
In fact, the volume of a pyramid is exactly one-third the volume of a prism that has the same height, base shape, and base size as the pyramid. The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
VOLUME OF A PYRAMID
The volume V of a pyramid is one-third the area of its base B times its height h.
V = Bh13
Find the volume of the pyramid.
Additional Example 1A: Finding the Volume of a Pyramid
A.V = 1
3Bh Use the formula.
B = 5 · 6 = 30 Find the area of the rectangular base.
V = 13 · 30 · 3 Substitute for B and h.
V = 30
The volume is 30 ft3.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
5 ft6 ft
3 ft
Multiply.
Additional Example 1B: Finding the Volume of the Pyramid
Find the volume of the pyramid.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
B. V = 13
Bh Use the formula.
B = 2 · 3 = 3 Find the area of the triangular base.
V = 13 · 3 · 5
V = 5
The volume is 5 cm3.
Multiply.
Substitute for B and h.
12
·
Find the volume of the pyramid.
Try This: Example 1A
A.V = 1
3Bh Use the formula.
B = 9 · 7 = 63 Find the area of the rectangular base.
V = 13 · 63 · 4 Substitute for B and h.
V = 84
The volume is 84 ft3.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
9 ft7 ft
4 ft
Multiply.
Try This: Example 1B
Find the volume of the pyramid.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
B. V = 13
Bh Use the formula.
B = 3 · 8 = 12 Find the area of the triangular base.
V = 13 · 12 · 4
V = 16
The volume is 16 m3.
Multiply.
Substitute for B and h.
12
·
h = 8 m3 m
h = 4 m
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
9-3 Volume of Pyramids, Cones, and Spheres
VOLUME OF A CONE
The volume V of a cone is one-third the area of its base, r2, times its height h.
V = r2h13
Find the volume of a cone to the nearest tenth. Use 3.14 for .
Additional Example 2: Finding the Volume of a Cone
V =13 r2h
V 13 · 3.14 · 52 · 6
V 157
The volume is about 157.0 yd3.
Use the formula.
Substitute.
Multiply.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Find the volume of a cone to the nearest tenth. Use 3.14 for .
V =13 r2h
V 13 · 3.14 · 22 · 3
V 12.56
The volume is about 12.6 yd3.
Use the formula.
Substitute.
Multiply.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Try This: Example 2
3 yd
2 yd
04/14/11 Volume #16
Today’s Plan:-Warm-up & Correct Homework-Volume-Assignment
Period 1: Page 482 #1-6
For each problem show the formula, substitution, and answer with units.
LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.
04/14/11 Volume #16
Today’s Plan:-Warm-up & Correct Homework-Volume-Assignment
Period 5: Finish both sides of worksheet for homework.
For each problem show the formula, substitution, and answer with units.
LT: I will calculate the volume of prisms, cylinders, pyramids, and cones.
