# Chapter 10

## All formulas in Chapter 10

Area of parallelogram: A=bh

Area of trapezoid: A=1/2(b1+b2)h

Area of circle: A=πr²

Surface area of a prism: S=2B+Ph

Surface area of a cylinder: S=2B+Ch

Lateral area of a cylinder: S=2πrh

Surface area of a pyramid: S=B+1/2*Pl

Surface area of a cone: S=πr²+πrl

Lateral area of a cone: S=πrl

Surface area of a sphere: S=4πr²

Volume of a prism: V=Bh

Volume of a cylinder: V=Bh

Volume of a pyramid: V=1/3*Bh

Volume of a cone: V=1/3*Bh

Volume of a sphere: V=4/3πr³

## Area of parallelograms and trapezoids

Vocabulary
~Base of a parallelogram- The length of any one of a parallelogram's sides..
~Height of a parallelogram- The perpendicular distance between the base and the opposite side.
~Bases of a trapezoid- The two parallel sides.
~Height of a trapezoid- The perpendicular distance the two bases.

Formulas:
Parallelogram: A=bh
Trapezoid: A=(b1+b2)h

**b1= base one, b2= base two, h= height**

## Real life example

You are re-roofing your house the roof is in the shape of a trapezoid, and you need to know how many squares of shingles you need. You can use the formula for area of a trapezoid to find just the right amount of shingles. (Ex. b1= 30ft, b2= 35ft, h=15ft.)

## Area of circles

Vocabulary
~Area- The amount of surface the figure covers.
~Circle- The set of all points in a plane that are the same distance from a fixed point called the center.
~Radius- The 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- A non- terminating decimal that with any circle it is the circumference divided by its diameter.

Formulas:
A=πr²

## Real life example

You are watering your grass using a rotating sprinkler. The sprinkler rotates in a complete circle. It sprays water at most 10 feet away(radius). Find the area of the yard that gets watered.
Area of a circle

## Three dimensional figures

Vocabulary
~Solid- A three-dimensional figure that encloses a part of space.
~Polyhedron- A solid that is encloses by polygons.
~Faces- The polygons that form a polyhedron.
~Prism- A polyhedron with two congruent bases that lie in parallel planes. The other faces are rectangles.
~Pyramid- A polyhedron with one base. The other faces are triangles.
~Cylinder- A solid with two congruent circular bases that lie in parallel planes.
~Cone- A solid with one circular base.
~Sphere- A solid formed by all points in space that are the same distance from a fixed point called the center.
~Edge- Where faces of a polyhedron meet.
~Vertex- A point where three or more edges meet.

## Surface area of prisms and cylinders

Vocabulary
~Net- A two-dimensional pattern that when folded forms a solid.
~Surface area- The sum of the areas of a polyhedrons faces.
~Lateral surface area- The surface area of a three-dimensional figure excluding the area of its bases.

Formulas:
Prism: S=2B+Ph
Cylinder: S=2B+Ch
S=2πr²+2πrh
lateral area of cylinder: 2πrh

**S=Surface area, B= Area of the objects base, P= Perimeter of the base, h=height**

## Real life example

You are designing a new product that has to be in the shape of a cylinder. You are making a label for the outside.The radius of the cylinder is 5in and the height is 12in. Use lateral surface area to make sure the label fits the container.

## Surface area of pyramids and cones

Vocabulary
~Slant height- The height of a lateral face, which is any face that is not a base.

Formulas:
Pyramid: S=B+1/2*Pl
Cone: S=πr²+πrl
Lateral surface area of a cone: S=πrl

**S= Surface area, B= Area of the objects base, P= perimeter of the base, l= slant height**

## Real life example

You are remolding the interior part of your house and there is a part of your house where the roof shape is a cone. You need to know the lateral surface area of the cone so you can paint the inside.The slant height is 12ft and the diameter is 6ft.
Surface Area Of A Cone - Slant Height Not Given

## Volume of prisms and cylinders

Vocabulary
~Volume- A measure of the amount of space it occupies.

Formulas:
Prism: V=Bh
Cylinder: V=Bh
V=πr²*h

**V= Volume, B= Area of base, h= height**

## Real life example

You are a delivery driver for Wal-Mart and you need to know how many boxes of soda will fit in the trailer. You are going to need to find the volume of the semi trailer and the volume of the boxes of soda. (Semi length 7.50ft, width 15ft, height 7.50ft. Soda box length, height, width are all 2.50ft)

## 10.7

Cylinder Volume and Surface Area

## Volume of pyramids and cones

Vocabulary
~Pyramid- A polyhedron with one base. The other faces are triangles.
~Cone- A solid with one circular base.
~Volume- A measure of the amount of space it occupies.

Formulas:
Pyramid: V=1/3*Bh
Cone: V=1/3*Bh
V=1/3*πr²*h

**V= Volume, h= height**

## Real life example

You are visiting the Egyptian pyramids and would like to know the volume so you can actually know how much space one pyramid takes up. The sides are 230m and the height is 150m.

## Surface area and volume of spheres

Vocabulary

~Sphere- A solid formed by all points in space that are the same distance from a fixed point called the center.

~Volume- A measure of the amount of space it occupies.

Formulas:

S=4πr²
V=4/3*πr³