MASTERSHEET
Copy/Paste Formulae for Chapter 10

>Copy the formula you need
>Paste it into the other workbook you are using
>Type into the pink boxes as instructed in your other workbook
>NOTE: Do NOT alter the formulae in this workbook, these are your templates only.

1.  Pythagoras To solve for an unknown side in a right-angled triangle when given  two sides.

Solve[(("hyp")^2)==(("one side")^2)+(("other side")^2)]//N

2. Pythagoras in 3D (use the below shape to visualise your 3D Pythagoras Problem)

To Find the slant height of a cone

Solve[(("slant height")^2)==(radius^2)+(height^2)]//N

3. To Find the height of a rectangle based pyramid

Solve[(("the longest slant height")^2)==((((length/2)))^2)+((((width/2)))^2) +(height^2)]//N

4. To Find the Space Diagonal of a 3 D Prism

Solve[(("space diagonal of prism")^2)==(length^2)+(height^2)+(width^2)]//N

5. Perimeter: add all side lengths of the shape

6. AREA FORMULAE

a. Area of a Rectangle

Solve[Area==length*width]//N

b. Area of a Parallelogram

Solve[Area==base*height]//N

c. Area of a Trapezium

Solve [Area==0.5* (a+b)*height]//N

d. Area of a Triangle

Solve[Area==0.5*base*height]//N

e. HERONS FORMULA (Area of a Triangle when you know all three side-lengths) =

s:=("first side length"+"second side length"+"third side length")/2//N
Solve[Area==(Sqrt[s(s-"first side length")*(s-"second side length")*(s-"third side length")])]//N

7. CIRCLE RELATED FORMULAE

a. Area of a Circle

Solve[Area==π * (radius^2)]//N

b. Circumference (perimeter) of a Circle when given radius

Solve[Circumference==2*π*radius]//N

c. Circumference (perimeter) of a Circle when given diameter

Solve[Circumference==π*diameter]//N

d. Finding the annulus

Solve[annulus=="area of large circle"-"area of small circle"]//N

e. Finding the arc of a circle

Solve[arc==radius*(("given angle"/180)*π)]//N

f. Finding the sector of a circle

Solve["sector"==(radius^2)*(("given angle"/360)*π)]//N

8. VOLUME FORMULAE

a. Volume of Rectangular Prism

Solve[volume==length*width*height]//N

b. Volume of Square Prism

Solve[volume==(length^3)]//N

c. Volume of Triangular Prism

Solve[volume==0.5*base*height*length]//N

d. Volume of Triangular Prism by Herons Formula

s:=("first side length"+"second side length"+"third side length")/2//N
Solve[volume==(Sqrt[s(s-"first side length")*(s-"second side length")*(s-"third side length")])*length]//N

e. Volume of Trapezium Prism

Solve[volume==0.5* (a+b)*height*length]//N

f. Volume of Cylinder

Solve[volume==π * (radius^2) * height]//N

g. Volume of Cone when given radius

Solve[volume==(1/3) * π *(radius^2) * height]//N

h. Volume of Cone when given diameter

Solve[volume==(1/3) * π *((((diameter/2)))^2) * height]//N

i. Volume of a Pyramid

Solve[volume==(1/3)*"length of base"*"width of base"*height]//N

j. Volume of a Sphere

Solve[volume==(4/3) * π *(radius^3) ]//N

k. Volume of a Hemisphere

Solve[volume==0.5*( (4/3) * π *(radius^3) )]//N

9. SURFACE AREA FORMULAE

a. Surface area of a Cube

Solve["Surface area"==6*(length*width)]//N

b. Surface area of a Square-based Pyramid

Solve["Surface area"==(length^2) + (4*"area of triangle face")]//N

c. Surface area of a Rectangular Prism

Solve["Surface area"==length*width *2+ length*height *2+height*width *2]//N

d. Surface area of Cylinder

Solve["Surface area"==(2*π*(radius^2)) +(2*π * radius* height)]//N

e. Surface area of a Cone

Solve["Surface area"==(π * (radius^2)) + (π * radius * "slanted side of cone")]//N

f. Surface area of Sphere

Solve["Surface area"==4*π * (radius^2)]//N

g. Surface area of HemsSphere

Solve["Surface area"==3*π * (radius^2)]//N

10. SCALE FACTORS AND SIMILARITY

a. Scale Factor (k)

Solve[k==(("side length of big image")/("side length of small image"))]//N

b. Area Scale Factor ((k^2))

(("area of big image")/("area of small image" ))//N

c. Volume Scale Factor ((k^3))

(("volumn of big image")/("volumn of small image"))//N

d. Using Scale Factor to find unknown side lengths

Solve[(("side length of big image")/("side length of small image"))==(("side length of big image")/("side length of small image"))]//N