# Chapter 10

## ALL EQUATIONS

10-1

Area of a Parallelogram: A=bh

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

10-2

Area of a circle: A=(π)r2

Area of a triangle: A=1/2*b*h

10-4

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

Surface area of a cylinder: S=2b=Ch or S=2(π)r2+2(π)rh

10-5

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

Surface area of a cone: S=(π)r2+(π)rl

10-6

Volume of a Prism: V=Bh

Volume of a Cylinder: V=Bh or V=(π)r2h

10-7

Volume of a pyramid: V=1/3Bh

Volume of a cone: V=1/3Bh or V=(π)r2h

Volume of a sphere: V=4/2(π)r3

Extension of Section 7

Volume of a sphere: 4/3*π*r3

## Vocab words that are used in this section(:

Base of a parallelogram: The length of any of the parallelograms sides.

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

Bases of a trapezoid: Any two parallel sides of the trapezoid.

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

## MAIN FORMULAS USED IN THIS SECTION

Area of a parallelogram: in words the formula for the area of a parallelogram is the answer or product of the base and the height together. The actual formula is the same as the area of a square A=bh

The formula is the same for a square because all a parallelogram really is, is a rectangle tilted. You could think that it got hit by Mr. Chitwoods sister and is now crooked because she ran into it with her car. Picture example below:

Area of a Trapezoid: in words, the area of a trapezoid is 1/2 the product of the sum or answer of the two bases and height. The formula is A=1/2(b1+b2)h

the little b stands for one base and the h stands for height.

## Vocab words that are used in this chapter(:

Area: The number of square units covered by a figure.

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: The sixteenth letter of the Greek alphabet ( Π, π ), transliterated as ‘p.’

## FORMULAS USED IN THIS SECTION

Circumference of a circle: In words the circumference of a circle is the product or answer of pi (π) and the diameter. As a formula the circumference of a circle is C=π*d or C=2*π*r

The little d stands for diameter while the r stands for radius.

Area of a Circle: In words, the area of a circle is the product or answer of pi (π) and the square of the radius. In a formula the area of a circle is written as A=π*r2

I already showed you where the radius is above.

## Vocab found in this section(:

Solid: a three-dimensional figure that encloses a part of space.

Polyhedron: A solid that is enclosed by polygons. Polyhedrons has only flat surfaces.

Faces: Polygons that form a polyhedron.

Prism: Is a polyhedron. Prisms have two congruent bases that lie in parallel planes. The other faces are rectangles. The cube is a prism with six square faces.

Pyramid: A pyramid is a polyhedron. Pyramids have one base. The other faces are triangles.

Cylinder: A solid with two congruent circular bases that lie in parallel planes.

Cone: A cone is a solid with one circular base.

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

Edge: Segments where faces of a polyhedron meet.

Vertex: A point where three or more edges meet.

## Vocab seen in this section(:

Net:
A two-dimensional pattern that forms a solid when it is folded.

Surface Area: The sum of the areas of its faces.

## MAIN FORMULAS USED IN THIS SECTION

Surface area of a prism: In words the surface area of a prism is the sum of twice the area of a base (B) and the product of the base's perimeter (P) and the height (h). The formula used to find the surface area of a prism is S=2B+Ph

Surface area of a Cylinder: In words, the surface area of a cylinder is the sum of twice the area of a base (B) and the product of the base's circumference (C) and the height (h). The formula for the surface area of a cylinder is S=2B+Ch or 2*π*r2+2*π*r*h

## Vocab seen in this section(:

Slant height: the height of a lateral face, that is, any face that is not the base.

## FORMULAS USED

Surface area of a Pyramid: In words the surface area of a regular pyramid is the sum of the area of the base (B) and one half the product of the bases perimeter (P) and the slant height (l). The formula for finding the surface area of a pyramid is S=B+1/2*P*l

Surface area of a Cone: In words the surface area of a cone is the sum of the area of the circular base with the radius(r) and the product of pi (π), the radius (r) of the bases, and the slant height (l). The formula for the surface area of a cone is S=π*r2+π*r*l

## Vocab seen in this section(:

Volume: A measure of the amount of space a solid occupies.

## FORMULAS USED

Volume of a Prism: In words the volume of a prism is the product of the area of the base(b) and the height (h). The formula for the volume of a prism is simply V=B*h

Volume of a Cylinder: The product of the area of a base (B) and the height (h). The formula for the volume of a cylinder is V=B*h or V=π*r2*h

## Vocab seen in this section(:

Pyramid, Cone, and Volume. These words were used in section 5 and 6

## FORMULAS USED

Volume of a Pyramid: In words the volume (V) of a pyramid is one third the product of the area of the base (B) and the height (h). The formula used for the volume of a pyramid is V=1/3*B*h

Volume of a Cone: In words the volume of a cone is one third the product of the area of the base (B) and the height (h). The formula for the volume of a cone is V= 1/3*B*h or V=1/3*π*r2*h

## Vocab seen in this extension(:

Sphere and volume that is seen in section 5 and 6.

## FORMULAS USED

Volume of a Sphere: In words the volume (V) of a sphere is four thirds the product of pi and the cube of the radius (r). The formula for the volume of a sphere is V=4/3*π*r3

## 3 Videos on how the formulas could work in real life.

• This video shows you why ice cream workers have to know the volume and surface area of the ice cream holder, cone, and ice cream. It also involves man formulas.
• This video shows you how people need to know the hypotenuse in real life, such as making a ramp.
• This video shows you how people use surface area in painting a room or object.