TechMathII - 2.6 - Area and Surface Area Day2

Bell Ringer

1. Find the area and Circumference:

2. Find the area of the trapezoid

10 in.

A = ½ * height * (b1 + b2)

20

2523

30

Objects that have length, width and depth are three-dimensional objects.

Definitions:

A three-dimensional closed object formed by Polygons is called a Polyhedron.

face face

base

Each polygon that forms the polyhedron is called a face.

The top and bottom faces are called Bases.

Surface Area

The Surface area (SA) of a three-dimensional figure is the sum of the areas of each face of the figure.

11 in

6 in8 in

If you wanted to gift-wrap this box you would need to find the surface area:

SA= Area of Area of two Area of two two bases + 6*11 faces + 8*11 faces

2 (8*6) + 2 (6*11) + 2(8*11) 2 ( 48) + 2 (66) + 2 (88) 96 + 132 176 404 in square

SURFACE AREA

Find the Surface area of the following:

6ft

7ft

12 ft

3in

3in

6in11 in

L=24 in W=18inh = 7in

You try!

A Prism is a polyhedron that has two parallel polygons bases and the other faces are parallelograms.

Volume of a rectangular box

If the rectangular box were filled with 1 cm cubes, there would be 6 x 2 cubes in the bottom layer and there are 3 layers. V = (Area of Base) * hSo: Volume = (L * W) * h = (6 * 2) * 3 = 12 * 3 = 36 cm³

IF you wanted to fill this box with packing peanuts, you would need to know the volume of the box. To find this you find the area of the base then multiplyIt by the height of the box.

11 in

8 in6 in

(8 * 6) 11 (48) 11 528 cubic inces

VOLUME

You try!

Find the Volume of: Water it will take to fill a rectangular fish tank:

50 inches in length, 20 inches in width that you will fill to 8 inches in depth.

Air enclosed in a speaker box that is 52 inches high, 23 inches wide and 18 inches deep.

Cylinders

A cylinder is a three-dimensional figure that consists of two parallel, congruent circular bases and a lateral surface that connects the boundaries of the bases.

http://www.teachertube.com/members/viewVideo.php?video_id=10174&title=Mr_Blue__s_Total_Surface_Area

TO FIND THE SURFACE AREAOF A CYLINDER:

You have two congruent circles and one rectangle (the length of the rectangle is the circumference of the circle)

SA= 2πr² + 2πrh Area of 2 circles + Circumference times height

EXAMPLEThis soup can has a diameter of 2.625 inchesand a height of 3.875 inches.

To find the Surface area and volume the soup can:

First find the radius of the can 2.625 = 1.3125 2 Next use the Next use the Surface area formula:

SA= 2πr² + 2πrhSA= (2 * 3.14 * 1.3125²) + (2 * 3.14 * 1.3125 * 3.875)SA = 10.82 + 31.94SA = 42.76

Next use the formula to fine the Volume: (area of the base times height)

V = Bh = πr²hV = 3.14 * 1.3125² * 3.875V = 20.96

You Try: Find the area and volume

Diameter is 22 metersHeight is 53 meters

SA= 2πr² + 2πrh

V = Bh = πr²h

Surface Area and Volume of a Sphere

Example:

SA = 4πr² V = 4/3 πr³

SA=(4)(3.14)(3²) V = 4/3 * 3.14 * 3³

SA=(4) (3.14)(9) V = 4/3 * 3.14 * 27

SA = 113.04 ft² V = 113.04 cubic feet

The radius of the Weather balloon is 3 feet

You Try!

Find the Surface Area and Volume of a Basketball with a radius of 50 cm.

SA = 4πr² V = 4/3 πr³

Surface Area and Volume of a Prism

SA = the sum of the area of the base and the faces

V = Bh (where B is the area of the base and h is the height)