04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Warm-Up LT: I will...

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.


Start working on the volume side of the pink worksheet. Show your formula, substitution, and answer for each problem.

04/14/11 Volume #16


Problem Solving Page


04/14/11 Volume #16


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?


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


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


5 ft6 ft

3 ft

Multiply.

Additional Example 1B: Finding the Volume of the Pyramid


Course 2


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

·


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 ft7 ft

4 ft

Multiply.

Try This: Example 1B


Course 2


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


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


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


Try This: Example 2

3 yd

2 yd

04/14/11 Volume #16


Period 1: Page 482 #1-6

For each problem show the formula, substitution, and answer with units.


04/14/11 Volume #16


Period 5: Finish both sides of worksheet for homework.

For each problem show the formula, substitution, and answer with units.


04/14/11Volume#16 Today’s Plan: -Warm-up & Correct Homework -Volume -Assignment Warm-Up LT: I will...

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