M1A Warm Up: Just try this and see if you can remember… The distance from Raleigh to Wilmington is 120 miles, the distance from Wilmington to Charlotte is 200 miles, and the distance from Raleigh to Charlotte is 160 miles. Do the three towns form a right triangle? Explain. Yes; The Pythagorean Theorem is true for these three values = 200 2

Homework Check: Document Camera

Objective: Students will be able to: Use formulas for rectangles, triangles, circles, cylinders, cones. To solve literal equations

What is the area formula?

bh

Rectangle Square 10m 17m 14cm

Rectangle Square 10m 17m 14cm 196 cm m 2

So then what happens if we cut a rectangle in half? What shape is made?

So then what happens if we cut a rectangle in half? What shape is made?

So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles

So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula?

So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula?

So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula? bh

So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula? bh 2

Triangle 5 ft 14 ft

35 ft 2 Triangle 5 ft 14 ft

A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. A cylinder has two circular bases.

Area of a Circle The Area (A) of a Circle is found by solving the following formula:

7 cm Find the area of the circle. A = π r 2 1. Substitute the radius into formula. A = π (7) 2 2. Use 3.14 as an approximation for π. A = 3.14(49) A = cm 2 3. Don't forget to label the units as square units.

What is the Area (A) of a Circle with a radius (r) of 8 m? 8 m

What is the Area (A) of the circle?

VOLUME OF PRISMS AND CYLINDERS WordsNumbersFormula Prism: The volume V of a prism is the area of the base B times the height h. Cylinder: The volume of a cylinder is the area of the base B times the height h. B = 2(5) = 10 units 2 V = 10(3) = 30 units 3 B =  (2 2 ) = 4  units 2 V = (4  )(6) = 24   75.4 units 3 V = Bh = (  r 2 )h

Show Brainpop video on Cylinders.Brainpop video

Ex 1: Find the volume of each figure to the nearest tenth. A rectangular prism with base 2 cm by 5 cm and height 3 cm. = 30 cm 3 B = 2 5 = 10 cm 2 V = Bh = 10 3 Area of base Volume of a prism

Ex 2: Find the volume of the figure to the nearest tenth. 4 in. 12 in. = 192  in 3 B =  (4 2 ) = 16  in 2 V = Bh = 16  12 Area of base Volume of a cylinder

A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.

VOLUME OF PYRAMIDS AND CONES (2 2 )

1313 V = 9 10 V = 30  94.2 in 3 V = Bh 1313 B = (3 2 ) = 9 in 2 Use 3.14 for . Ex 7: Find the volume of the figure.

Solving Formulas WS Complete the front with Mrs. Childrey

Literal Equations This means to solve an equation for one variable in terms of another variable.

1) Solve 2x - 4y = 7 for x To get x by itself, what is the first step? 1. Add 2x 2. Subtract 2x 3. Add 4y 4. Subtract 4y Answer Now

L1) Solve 2x - 4y = 7 for x

1. Draw “the river” 2. Add 4y to both sides 3. Simplify 4. Divide both sides by 2 5. Does it simplify? + 4y + 4y 2x = 7 + 4y 2 2 x = 2y + 3.5

L2) Solve 2x - 4y = 7 for y To get y by itself, what is the first step? 1. Add 2x 2. Subtract 2x 3. Add 4y 4. Subtract 4y Answer Now

L2) Solve 2x - 4y = 7 for y 1.Draw “the river” 2.Subtract 2x from both sides 3.Simplify 4.Divide both sides by -4 5.Does it simplify? - 2x -4y = 7 - 2x y = 0.5x

L3) Solve for y. What is the first step? 1. Multiply by 3 2. Divide by 3 3. Add a 4. Subtract a Answer Now

L3) Solve for y: 1.Draw “the river” 2.Clear the fraction – multiply both sides by 3 3.Simplify 4.Subtract a from both sides 5.Simplify y + a = 3c -a -a y = 3c - a

L4) Solve for y: 4x – 2y = x x x x - 6 Answer Now

L4) Solve for y: 4x – 2y = 12 1.Draw “the river” 2.Subtract 4x from both sides 3.Simplify 4.Divide both sides by -2 5.Does it simplify? - 4x -2y = 12 – 4x y = x or y = 2x - 6 Yes!

1. L = V - WH L5) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L? Answer Now

1. h = 3Vb L6) The formula for the volume of a pyramid is V =. Which equation solves the formula for h? Answer Now

Classwork: Literal equations part 1 #1-12

Homework: Literal Equations #11 and 12 And Back of Solving Formulas WS