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Chapter 7Lesson 7-6

A. AB. BC. CD. D

A. cube; 6 faces, all squares; 12 edges; 8 vertices

B. cube; 4 faces, all squares; 12 edges; 8 vertices

C. cube; 4 faces, all squares; 8 edges; 12 vertices

D. cube; 6 faces, all squares; 8 edges; 12 vertices

Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices.

(over Lesson 7-4)

1. A2. B3. C4. D

A. rectangular prism; 4 faces, all rectangles; 12 edges; 8 vertices

B. rectangular prism; 4 faces, all rectangles; 8 edges; 12 vertices

C. rectangular prism; 6 faces, all rectangles; 12 edges; 8 vertices

D. rectangular prism; 6 faces, all rectangles; 8 edges; 12 vertices

Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices.

(over Lesson 7-4)

1. A2. B3. C4. D

A. 25.5 cm3

B. 51 cm3

C. 76.5 cm3

D. 153 cm3

Find the volume of the given solid. Round to the nearest tenth if necessary.

(over Lesson 7-5)

1. A2. B3. C4. D

A. 91.1 ft3

B. 45.6 ft3

C. 20.1 ft3

D. 13.5 ft3

Find the volume of the given solid. Round to the nearest tenth if necessary.

(over Lesson 7-5)

Last week you were asked to reflect upon how you participated in each of the lessons and write a goal for the lesson of the day.

Today’s lesson is about volume. For this lesson try drawing at least one 3-dimensional shape to help you better visualize the concept.

• cone

• Find the volumes of pyramids and cones.

Standard 7MG2.1Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

Prior Knowledge:The volume of a rectangular prism with a base length of 4in, a width of 2in, & a height of 3in = 24in3.

V = 24in3

Something to Ponder:The volume of a rectangular pyramid with a base length of 4in, a width of 2in, & a height of 3in = 8in3.

4 in2 in

3 in

4 in

3 in

2 in

V = 8in3

New Knowledge:Is there a relationship between the volume of a prism & a pyramid?

Let’s investigate!

8 in3 in

4 in

8 in

4 in

3 in

V = 96in3 V = 32in3

3 in1 in

6 in

3 in

6 in

1 in

V = 18in3 V = 6in3

Compare the dimensions of each prism and pyramid & their volume.

Is there a relationship between them?

Find the Volume of a Pyramid

The volume formula of a pyramid is:

You must always begin a calculation such as this by 1st identifying the:

_______________________________________________

Base of the Pyramid

The base of this Pyramid is a:

_______________________________________________Rectangle

Finding the volume of any 3-dimensionalsolid requires that you write the formula for the ________ of the base of the solid.

area

The base of this Pyramid is a rectangle. The formula for the area of a rectangle is:

_______________________________________________A = l w or A = 7cm

3cm

Find the Volume of a Pyramid

The volume of a pyramid is:

Now that we have the area of the base (21cm2) we have to multiply that times the ________ of the base of the pyramid.

height

The height of this Pyramid is 20cm. 21cm2 20cm =

_______________________________________________

420cm3

Find the Volume of a Pyramid

The volume of a pyramid is:

Now that we have the area of the base multiplied times the area of the base, we need to ________ that by 3 to get our final answer.

divide

The volume of this Pyramid is 420cm3. 420cm2 ÷ 3 =

_______________________________________________

140cm3

Find the Volume of a Pyramid

The volume of a pyramid is:

Find the Volume of a Pyramid

Find the volume of the pyramid.

Answer: The volume is 140 cubic centimeters.

Volume of a pyramid

Simplify.

B = 7 ● 3, h = 20

A. AB. BC. CD. D

A. 60 m3

B. 72 m3

C. 80 m3

D. 120 m3

Find the volume of the pyramid.

1. A2. B3. C4. D

TOYS A company is designing pyramid shaped building blocks with a rectangular base. They want the volume of the blocks to be 18 cubic inches. If the length of the side of the base is 6 inches and the width of the side of the base is 3 inches what should be the height of the blocks?3

3

3

3 in 6 in

h in

Start by plugging in data to the formula:

V = ⅓ Bh

18 = ⅓ (6 3)h

1. A2. B3. C4. D

Now use the data and solve for h, the height.

3

3

3

3in 6in

Xin 18 = ⅓ (6 3)h

1. A2. B3. C4. D

A. 6 in.

B. 6.5 in.

C. 3 in.

D. 3.5 in.

3

3

3

3in 6in

Xin

TOYS A company is designing pyramid shaped building blocks with a rectangular base. They want the volume of the blocks to be 18 cubic inches. If the length of the side of the base is 6 inches and the width of the side of the base is 3 inches what should be the height of the blocks?

Prior Knowledge:The volume of a rectangular pyramid is ⅓ that of a rectangular prism with the same dimensions.

Fact:- The formula for the volume of a rectangular prism is: V

= Bh

4 in

3 in2 in

V = 8in3

-The formula for the volume of a rectangular pyramid is:V = ⅓Bh

4 in

2 in

3 in

V = 24in3

4 in

3 in2 in

V = 8in3

4 in

3 in2 in

V = 8in3

=

=

+

+

+

+

Reflective Knowledge:

Considering the formula relationship between a rectangular prism (V= Bh) and a rectangular pyramid (V = ⅓Bh), do you think there is a similar relationship between a cylinder and a cone?

r

h

New Knowledge:

r

h

V = ⅓Bhor

V = ⅓(πr2)h

V = Bhor

V = (πr2)h

Find the Volume of a Cone

Find the volume of the cone. Round to the nearest tenth.

Answer: The volume is about 18.8 cubic meters.

Volume of a cone

Replace r with1.5 and h with 8.

Simplify.

1. A2. B3. C4. D

A. 28.5 in3

B. 29.2 in3

C. 34.1 in3

D. 37.7 in3

Find the volume of the cone. Round to the nearest tenth.

Reflect upon the lesson today. Ask yourself:“Did I make a connection between what I had learned previously with what I was taught today? Do I ever think about prior lessons and how they can help me with new lessons.

Write down how often you make a reflect back on a previous lesson you’ve had and how it has helped you make a connection with a new concept.

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