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Warm up #3 Page 11 draw and label the shape

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# Warm up #3 Page 11 draw and label the shape - PowerPoint PPT Presentation

Warm up #3 Page 11 draw and label the shape. 1 . The area of a rectangular rug is 40 yd 2 . If the width of the rug is 10 yd , what is the length of the rug? 2 . The perimeter of a square rug is 16yd . If the width of the rug is 4 yd , what is the length of the rug?

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Warmup #3 Page 11drawand labeltheshape

1. The area of a rectangular rug is 40 yd2. If the width of the rug is 10 yd, what is the length of the rug?

2. The perimeter of a square rug is 16yd. If the width of the rug is 4 yd, what is the length of the rug?

3. Jose wants new carpeting for his living room. His living room is an 9 m by 9 m rectangle. How much carpeting does he need to buy to cover his entire living room?

4. Patricia has a rectangular flower garden that is 10 ft long and 5 ft wide. One bag of soil can cover 10 ft2. How many bags will she need to cover the entire garden?

A Prism

Cylinder

Cuboid

Cross section

Triangular Prism

Trapezoid Prism

Volume of Prism = length xCross-sectional area

h

r

b

Area Rectangle

= Base x height

Area Circle = πr2

a

h

h

b

Area Trapezium

= ½ x (a + b) x h

b

Area Triangle

= ½ x Base x height

Area Formulae

### Geometry

Surface Area of Triangular and cuboid Prisms

Surface Area
• Triangular prism – a prism with two parallel, equal triangles on opposite sides.

To find the surface area of a triangular prism we can add up the areas of the separate faces.

h

w

l

Surface Area
• In a triangular prism there are two pairs of opposite and equal triangles.

We can find the surface area of this prism by adding the areas of the pink side (A), the orange sides (B), the green bottom (C) and the two ends (D).

8 cm

A

2 cm

B

5 cm

C

7 cm

Surface Area
• We should use a table to tabulate the various areas.

Example:

8 cm

A

2 cm

B

5 cm

C

7 cm

Surface Area
• We should use a table to tabulate the various areas.

Example:

8 cm

A

2 cm

B

5 cm

C

7 cm

Surface Area
• We should use a table to tabulate the various areas.

Example:

8 cm

A

2 cm

B

5 cm

C

7 cm

Surface Area
• We should use a table to tabulate the various areas.

Example:

8 cm

A

2 cm

B

5 cm

C

7 cm

Surface Area
• We should use a table to tabulate the various areas.

Example:

8 cm

A

2 cm

B

5 cm

D

C

7 cm

Surface Area
• We should use a table to tabulate the various areas.

Example:

8 cm

A

2 cm

B

5 cm

D

C

7 cm

Surface Area

Example:

B

• Now you try...find the surface area!

2m

C

2m

11m

2m

Surface area of a cuboid

To find the surfacearea of a shape, we calculate the total area of all of the faces.

A cuboid has 6 faces.

The top and the bottom of the cuboid have the same area.

Surface area of a cuboid

To find the surfacearea of a shape, we calculate the total area of all of the faces.

A cuboid has 6 faces.

The front and the back of the cuboid have the same area.

Surface area of a cuboid

To find the surfacearea of a shape, we calculate the total area of all of the faces.

A cuboid has 6 faces.

The left hand side and the right hand side of the cuboid have the same area.

Formula for the surface area of a cuboid

w

l

2 × lw

Top and bottom

Front and back

+ 2 × hw

h

+ 2 × lh

Left and right side

We can find the formula for the surface area of a cuboid as follows.

Surface area of a cuboid =

= 2lw + 2hw + 2lh

Surface area of a cuboid

To find the surfacearea of a shape, we calculate the total area of all of the faces.

Can you work out the surface area of this cuboid?

5 cm

8 cm

The area of the top = 8 × 5

= 40 cm2

7 cm

The area of the front = 7 × 5

= 35 cm2

The area of the side = 7 × 8

= 56 cm2

Surface area of a cuboid

To find the surfacearea of a shape, we calculate the total area of all of the faces.

So the total surface area =

5 cm

8 cm

2 × 40 cm2

Top and bottom

7 cm

+ 2 × 35 cm2

Front and back

+ 2 × 56 cm2

Left and right side

= 80 + 70 + 112 = 262 cm2

Chequered cuboid problem

This cuboid is made from alternate purple and green centimetre cubes.

What is its surface area?

Surface area

= 2 × 3 × 4 + 2 × 3 × 5 + 2 × 4 × 5

= 24 + 30 + 40

= 94 cm2

How much of the surface area is green?

48 cm2

Surface area of a prism

What is the surface area of this L-shaped prism?

3 cm

To find the surface area of this shape we need to add together the area of the two L-shapes and the area of the 6 rectangles that make up the surface of the shape.

3 cm

4 cm

6 cm

Total surface area

= 2 × 22 + 18 + 9 + 12 + 6

+ 6 + 15

5 cm

= 110 cm2

Using nets to find surface area

6 cm

3 cm

3 cm

6 cm

5 cm

3 cm

3 cm

Here is the net of a 3 cm by 5 cm by 6 cm cuboid

Write down the area of each face.

Then add the areas together to find the surface area.

18 cm2

15 cm2

15 cm2

30 cm2

30 cm2

18 cm2

Surface Area = 126 cm2

Surface Area
• Cylinder – (circular prism) a prism with two parallel, equal circles on opposite sides.

To find the surface area of a cylinder we can add up the areas of the separate faces.

Surface Area
• In a cylinder there are a pair of opposite and equal circles.

We can find the surface area of a cylinder by adding the areas of the two blue ends (A) and the yellow sides (B).

A

B

Surface Area
• We can find the area of the two ends (A) by using the formula for the area of a circle.
• A = π r2

B =10

a

5

Surface Area
• Sketch cylinder and copy table. Work together to find the S.A.
Surface Area
• Sketch cylinder and copy table. Calculate S.A.
• Assignment

4m

2m

A

A

Volume Cylinder

Area = π x r2

= π x 32

= π9cm2

3cm

5cm

Volume = length x Area

= 5 x π9cm2

= 5 x π x 9cm2

= 45 x π

=45π

Lets do these together. Find the volume.

V = r2h

16

Volume of a Cylinder

The volume, V, of a cylinder is V = Bh = r2h, where B is the area of the base, h is the height, and r is the radius of the base.

6cm

4cm

2cm

5cm

Volume Trapezoid Prism

trapezoid Area = ½ x(a + b) x h

= ½ x (6 + 2)x 5

= ½ x 40cm2

= 20cm2

Volume = length x area

= 20x 4

= 80cm3

8cm

4cm

2cm

4cm

Volume Trapezoid Prism

trapezoid Area = ½ x(a + b) x h

= ½ x (8 + 3)x 4

= ½ x cm2

= 20cm2

Volume = length x area

= 20x 4

= 80cm3

### Geometry

Volume of Rectangular and Triangular Prisms

Volume
• The same principles apply to the triangular prism.

To find the volume of the triangular prism, we must first find the area of the triangular base (shaded in yellow).

h

b

Volume
• To find the area of the Base…

Area (triangle) = b x h

2

This gives us the Area of the Base (B).

h

b

Volume
• Now to find the volume…

We must then multiply the area of the base (B) by the height (h) of the prism.

This will give us the Volume of the Prism.

B

h

Volume
• Volume of a Triangular Prism

Volume

(triangular prism)

V = B x h

B

h

Volume

Volume

V = B x h

• Together…
Volume

Volume

V = B x h

V = (8 x 4) x 12

2

• Together…
Volume

Volume

V = B x h

V = (8 x 4) x 12

2

V = 16 x 12

• Together…
Volume

Volume

V = B x h

V = (8 x 4) x 12

2

V = 16 x 12

V = 192 cm3

• Together…
Volume

Find the Volume

• Your turn…
Triangular Prism
• To find the volumeof a triangular prism find the area of the triangular base and multiply times the height of the prism. The height will always be the distance between the two triangles.

Volume Triangular Prism

Cross-sectional Area = ½ x b x h

= ½ x 8 x 4

= .5 x 32

= 16cm2

4cm

4.9cm

6cm

8cm

Volume = length x CSA

= 16 x 6

= 96cm3

Volume Cuboid

Cross-sectional Area = b x h

= 7 x 5

= 35cm2

5cm

10cm

7cm

Volume = length x CSA

= 10 x 35

= 350cm3

The box shown is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box? What is the volume of the box?Ex. 1: Finding the Volume of a rectangular prism

VOLUMES OF PRISMS AND CYLINDERS

Volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure.

1cm

How many 1cm3 cubes will fill the rectangular prism on the right

10

7

6

Find the volume.

Volume of a Prism

The volume, V, of a prism is V = Bh, where B is the area of the base and h is the height.

Find the volume.

V=s3

9 in.

9 in.

9 in.

Volume of a Cube

The volume of a cube is the length of its side cubed, or V=s3

Volume of a cuboid

Volume of a cuboid

= length × width × height

= lwh

We can find the volume of a cuboid by multiplying the area of the base by the height.

The area of the base

= length × width

So,

height, h

length, l

width, w

Volume of a cuboid

What is the volume of this cuboid?

Volume of cuboid

= length × width × height

5 cm

= 5 × 8 × 13

13 cm

8 cm

= 520 cm3

Volume of a prism made from cuboids

What is the volume of this L-shaped prism?

3 cm

We can think of the shape as two cuboids joined together.

3 cm

Volume of the green cuboid

4 cm

= 6 × 3 × 3 = 54 cm3

6 cm

Volume of the blue cuboid

= 3 × 2 × 2 = 12 cm3

Total volume

5 cm

= 54 + 12 = 66 cm3

Volume of a prism

Volume of a prism

= area of cross-section × length

Remember, a prism is a 3-D shape with the same cross-section throughout its length.

3 cm

We can think of this prism as lots of L-shaped surfaces running along the length of the shape.

If the cross-section has an area of 22 cm2 and the length is 3 cm,

Volume of L-shaped prism =

22 × 3 =

66 cm3

Volume of a prism

What is the volume of this prism?

12 m

4 m

7 m

3 m

5 m

Area of cross-section = 7 × 12 – 4 × 3 =

84 – 12 =

72 m2

Volume of prism = 5 × 72 =

360 m3