Review of Pythagorean Theorem and Volume

Review of Pythagorean Theorem and Volume

Why do we use the Pythagorean Thorem?

• Find missing side; given two sides

• Determine if a triangle is a right triangle

• Determine the distance between two points

Pythagorean Theorem Formula

a² + b²=c²

What is the perimeter of a right triangle with the hypotenuse of 30in and leg of 18in?

• Formula for perimeter of right triangle is the sum of all sides (a+b+c= P)

• Step 1: Find the missing side of the right triangle

• Step 2: Add the lengths of all sides to find perimeter

Multiple Choice

Which quadrant is point (-5,2) located?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

Understanding Points on a Coordinate Plane

Points are written (x,y)

Given point (7,5), which digit is my "x" ? Which is my "y" ?

Distance Formula

 $D=\sqrt{\left(x_2\ -\ x_1\right)\ ^2+\left(y_{2\ }-y_1\right)^2\ \ }$  

Open Ended

Plug the points into the right place...

A ( 3,-4) and B (6,0)

x₁₌

x₂₌

y₁₌

y₂₌

Volume

The amount of space a three- dimensional object occupies/ takes up.

* Measured in cubic units

Volume of a Prism

Find area of base and multiply by the height

Finding Area of Rectangle

• Area of rectangle = L x W

Multiple Choice

Find the volume:

• 720 in³

• 720 in²

• 720 in

• 240 in³

Multiple Choice

Find the volume

• 32 in³

• 384 in³

• 384 in²

• 96 in³

Words to consider when thinking of a circle

• Radius

• Circumference

• Pi

• Diameter

Volume of Cylinder

• First find the area of the base (circle)

• Multiply area of base by height

• Formula: Volume of cylinder= πr²h

Area of a circle

•  $A=\pi r^2$  

Multiple Choice

Find the area of the base

Bottom number:2
Side number: 4

• 8 in²

• 4 in²

• $4\pi$ in

Multiple Choice

Find the volume

Number on bottom: 2

Number on side: 4

• 16π in3

• 8π in3

• 4π in3

• 2π in²