SURFACE AREA & VOLUME What is Surface Area? Surface Area is the area of each surface of the...

SURFACE AREA&

VOLUME

What is Surface Area?

Surface Area is the area of each surface of the figure

You will have to find the area of each side of the figure and add them together

NOTE: all measurements will be squared!!! (since it’s area)

Surface Area Example

There are 6 rectangles in this prism. Find the area of all & add.

There are 6 rectangles in this prism. Find the area of all & add.11

in.

13 in.

12 in.

2 rectangles:A= L x WA= 13 x 11A= 143 in.2

• 143 + 143 + 132 + 132 + 156 + 156 = 862 in.2

2 rectangles:A= L x WA= 12 x 11A= 132 in.2

2 rectangles:A= L x WA= 13 x 12A= 156 in.2

Practice Problem 2Practice Problem 2• Find the surface area of the triangular prism shown to the right.• Find the area of each shape and add.

Area of the triangle #1A = ½ bhA = ½ (12)(16)A = 96 cm2

Area of the triangle #2A = ½ bhA = ½ (12)(16)A = 96 cm2

Area of the rectangle #1A = L x WA = 20 (10)A = 200 cm2

Area of the rectangle #2A = L x WA = 16 (10)A = 160 cm2

Area of the rectangle #3A = L x WA = 12 (10)A = 120 cm2

SA = 96 + 96 + 200 + 160 + 120

SA = 672 cm2

Practice Problem 3Practice Problem 3• Find the surface area of the cylinder. • There are 2 circles and 2 rectangles

in a cylinder

2 circles:A = r2

A = 62

A = 36A = 113.04

2 “rectangles”:A = rhA = (6)(18)A = 108A = 339.12

Surface Area = 113.04 + 113.04 + 339.12 + 339.12 = 904.32 in.2

What is Volume?

Volume is the measure of the capacity of a container.

It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc.

Cubic Units Volume is measured in cubic units.

Use cubes to fill a rectangular prism such as a box.

One Cubic Unit

1 unit(height)

1 unit(length)

1 unit(width)

A unit might be measured in inches, feet, centimeters,

etc.

A unit might be measured in inches, feet, centimeters,

etc.

Note: All measurements will be cubed! 14in.3

How many cubic units is this rectangle?

What did you find?

Yes, it is 8 cubic units!

How about this one?

Remember… there are some cubes you can’t

see!Yes! There

are 12 cubic units!

What’s the formula?

The formula for finding the volume of a rectangle is ….

Volume = L x W x HVolume = L x W x H

This means we take the This means we take the lengthlength times the times the width,width,

then multiply that by the then multiply that by the heightheight..

Let’s try it!

L = 3

H = 3

W = 2

3 x 3 x 2 = 18 cubic units

The Volume Of A Triangular Prism.Consider the triangular prism below:

5cm

8cm

5cm

Calculate the volume:Volume = ½ b h l

V = ½ (5)(5)(8)V = 100 cm3

The formula for the volume of a triangular prism is :

V = ½ b h l

B= base h = height l = length

The Volume Of A Cylinder.Consider the cylinder below:

4cm

6cm

Calculate the volume:

V = r 2 x h

V = x 2 x 2 x 6

V = 75.36 cm3

The formula for the volume of a cylinder is:

V = r 2 h

r = radius h = height.

What Goes In The Box ? 2Calculate the volume of the shapes below:

(1)

16cm

14cm

(2)

3m

4m

5m

(3)

6cm12cm

8m

2813.4cm3

30m3

288cm3