Mighty Measurements!

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Measurement: Length, Area, and Volume

Volume

Volume is the measure of the amount of space that is inside of a three dimensional shape.

Volume of a Sphere

V = 4/3 Pi r3

Volume of a cone

V = 1/3Bh

Volume of a Pyramid

V = 1/3Bh

Volume of a Cylinder is base x height

V = Bh

Volume = length x width x height

V = lwh

The Measurement Process

The International System (Metirc Units)

Temperature - Celsius

F boiling point minus F freezing point divided by C boiling point minus C freezing point

212 - 32 / 100 - 0 = 1.8 or 9/5

Celsius to Fahrenheit

F = 1.8C + 32

Metric Units of Area

Metric Units of Length, Capacity and Mass

The U.S. Customary System

Temperature - Fahrenheit

F boiling point minus F freezing point divided by C boiling point minus C freezing point

212 - 32 / 100 - 0 = 1.8 or 9/5

Fahrenheit to Celsius

C = 5/9 (F-32)

Units of Volume

Units of Area

Units of Length, Capacity and Weight

Surface Area

Surface area measures total area of the surface of a three dimensional shape.

Spheres

Surface area of a sphere

S = 4Pi r squared

Cones

Surface area of cones

SA = Pi r squared + Pi rs

Pyramids

Surface area of pyramids
SA = B + 1/2ps

Cylinders

Surface area of cylinders

SA = 2B + ph

B = area of base
p = perimeter of the base
h= height

Prisms

Surface area of prisms

SA = 2B + ph

B = area of base
p = perimeter of the base
h= height

Area and Perimeter

Irregular shapes

Circles

The perimeter of a circle is called circumference.

The diameter is the distance across a circle throuht the center.

The radius of a circle is the distance form the center of a circle.

The ratio of a circle's circumference to its diameter is called Pi. Pi = 3.14159.

Circumference = 2 times Pi times radius

C = 2 x Pi x r

Area of a Circle = Pi times the Radius squared

A = Pi x r x r

Polygons

Perimeter

The perimeter is the distance around a shape.

You will add the lenghs of all sides together.

Area

The area is the size of a surface within a perimeter.

Triangles

To find the the area if a triangle you will multiply the base by the height and then divide by 2 (since a triangle is half of a parallelogram)

Area of a Triangle =

1/2 x Base x Height or Base x Height / 2

A = 1/2bh or A = bh / 2

Trapezoids

Area of a Trapezoid = 1/2 (Base a + Base b) x Height

A = 1/2 (a + b)h

Parallelograms

Area of a Parallelogram = Base times Height

A = bh

Rectangles

Area of a Rectangle = Length times Width

A = lw