# Chapter 10

## Formulas

Area of rectangle: bh

Area of square: s^2

Area of circle: PI*r^2

Area of Triangle: 1/2*bh

Area of Trapezoid: 1/2*h(b1+b2)

Volume of Cube: l*w*h

Volume of Cylinder: PI*r^2*h

Volume of Rectangular Prism: w*h*l

Volume of Cone: 1/3*PI*r^2*h

Volume of Pyramid: 1/3*bh

Volume of Sphere: 4/3*PI*r^3

Surface area of sphere: 4*PI*r^2

Surface area of Pyramid: 2*bs+b^2

Surface area of Cone: PI*r (square root r^2+h^2)

Surface area of rectangular prism: 2(wl+hl+hw)

Surface area of Cylinder: 2*PI*r*h+2*PI*r^2

Surface area of Cube: 6*a^2

Area Formula Song - Fun Learning Math!

## 10.1

Vocabulary:

Base of a Parallelogram: The length of any one of its sides.

Height of a Parallelogram: The perpendicular distance between the base and the opposite side.

Base of a Trapezoid: The two parallel sides.

Height of a Trapezoid: The perpendicular distance between the bases.

## 10.2

Vocabulary:

Area (of circles): The product of pi and the square of the radius.

Circle: Set of all points in a plane that are the same distance from a fixed point.

Radius: Distance from the center to any point on the circle.

Diameter: The distance across the circle through the center, or twice the radius.

Circumference: The distance around the circle.

Pi: The constant repetition of a number represented by a Greek symbol.

## 10.3

Vocabulary:

Solid, Polyhedron, Face: Solid in 3 detentions with flat faces.

Prism: A solid geometric figure with two of the same faces.

Pyramid: A structure with triangle or rectangle base which points meet at the top.

Cylinder: A geometric figure with parallel sides with circle cross sections.

Cone: A solid that goes from a circular base to a point at the top.

Sphere: A round solid object that has every point from the center equidistant from the center.

Edge, Vertex: The outside limit of an object, where two edges meet.

## 10.4

Vocabulary:

Net: The unfolded area and shape of a 3D object.

Surface Area: The area of the undermost layer.

Nets of 3D-Shapes

## 10.5

Vocabulary:

Slant Height: The measurement of a cone or pyramid from the bottom to the top slanting up the shape.

## 10.6

Vocabulary:

Volume: The amount of space an object occupies.

Volume Song Video

## 10.7

Vocabulary:

Pyramid: A monumental structure with a square or triangular base with sloping sides that meet at the top in a point.

Cone: An object that starts with a circular base and slopes to a point at the top.

Volume: The amount of space an object occupies.

## Real Life Example

If you wanted to find the volume of the pyramids in Egypt, you would find the base length (l), the base width (w), and the height which is perpendicular from the base (h). Then you use the formula, B= 1/3*h. For example if the height was 100ft than you would multiply that by 1/3 and then that would give you (B) or the area of the base.

## Practice Problem

Question: find the area of a rectangle if its base is 4ft and it height is 30ft:

So you would start off with the formula, A=bh. Then plug in you numbers, 4*30. which would give you 120.