FORMULAS

Definitions

AreaPerimeter/CircumferenceSurface AreaVolumeDistance / RateSimple InterestDensity

Distance = Rate x Time

How far did you travel if you drove at a rate of 60 miles per hour for 5 hours?

D = rtD = 60 x 5D = 300

Answer: 300 miles

Time = Distance / Rate

How much time did it take for you to travel 300 miles at a rate of 60 miles per hour?

T = D/rT = 300 / 50D = 5

Answer: 5 hours

D = rt

Find D if r = 12 and t = 8

Find r if D = 240 and t = 8

D = rtD = 12 x 8D = 96

D = rt240 = r x 8Solve backwards240 / 8 = r 30 = r

D = rt240 = 8r 8 830 = r

Simple Interest I = PRT

Interest = Principle x Rate x Time

How much interest would you make if you deposited $500 at the bank

at a rate of 10% per year for 4 years?

I = 500 x .10 x 4

I = $200

Simple Interest I = PRTInterest = Principle x Rate x Time

How much time did you keep your money in the bank if you made

$400 in interest at a rate of 5% with an initial deposit of $800

( principle)?400 = 800 x .05 x t

400 = 40 x t

400 / 40 = 10 years

Simple Interest I = PRTHow much time did you keep your money in the

bank if you made $400 in interest at a rate of 5% with an initial deposit of $800 ( principle)?

I = PRT

400 = 800 x .05 x t

400 = 40 t

400 = 40 t

40 40

10 = t

Circumference of a Circle

PI TIMES DIAMETER

PI TIMES DOUBLE THE RADIUS

3.14 d

Circumference of a Circle

C = 3.14 d

31.4 unitsFind C if d = 10

Find C if d = 5 15.7 units

Find C if r = 5 31.4 units

Circumference of a Circle

C = 3.14 d

20 unitsFind d if C = 400

Substitute 400 for C

Solve backwards

3.14 times what is 400

Divide 400 by 3.14

C = 3.14 d

400 = 3.14 d

400 = 3.14 d

3.14 3.14

20 = d

Area of a Circle

PI TIMES RADIUS TO SECOND POWER

A = 3.14 r 2

A = 3.14 x r x r

Area of a Circle

A = 3.14 r 2

Find A if r = 10 314 square units

Find A if r = 5 78.5 square units

Find A if r = 20 1256 square units

Area of a Circle

A = 3.14 r 2

Find r if A = 2826 sq units

30 units

2826 = 3.14 x r2

Work backwards

Undo operations

Step by step

Divide by 3.14

Square Root

A = 3.14 r2

2826= 3.14 r2

2826 = 3.14 r2

3.14 3.14

900 = r2

30 = r

Surface Area of a Rectangular Prism

SA is double the area of the front + double the area of the side + double the area of the top

SA = 2 lw + 2 lh + 2 wh

SA = 2 lw + 2 lh + 2 wh

L = 10 cm

W = 5 cm

H = 6 cm

SA = 280 square centimeters

10 cm 5 cm

6 cm

SA = 280 square centimeters

SA = 2lw + 2lh + 2wh

SA = 2*10*5 + 2*10*6 + 2*5*6

SA = 100 + 120 + 60

Hint:

use every combination

Surface Area

Surface Area

Volume of a Rectangular Prism

V = lwh

L = 25 inches

W = 4 inches

H = 6 inches

600 cubic inches

Volume

25 inches4 inches6 inches

600 cubic inches

V = lwh

V = 25 * 4 * 6

V = 600 cubic inches

Volume of a Rectangular Prism

Density = Mass / Volume

Take a look at the two boxes above. Each box has the same volume. If each ball has the same mass, which box would weigh more? Why?

The box that has more balls has more mass per unit of volume. This property of matter is called density. The density of a material helps to distinguish it from other materials. Since mass is usually expressed in grams and volume in cubic centimeters, density is expressed in grams/cubic centimeter.

Density = Mass / Volume

4 cm

6 cm

5 cm

2. Calculate Mass:

Each marble weighs 10 grams

Box 1 contains 24 marbles

Box 2 contains 12 marbles

V = 120 cc

M = 240 g

M = 120 g

1. Calculate Volume: V = lwh

Density = Mass / Volume

4 cm

6 cm

5 cm

Calculate Density:

Volume = 120 cc

Mass 1 = 250 g

Mass 2 = 130 g

D = 2 D = 1

Calculate Density:

D = M/V

D = 240/120

D = 120/120