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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