# Chapter 10

### Isabel K

## 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

## Chapter 10: Section 1

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

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:

## A simple rectangle sitting on the side of the road | ## Suddenly Mr.Chitwoods sister comes driving past, looses control and runs into this rectangle sitting on the side. | ## That regular square is now hurt and ends up tilting just like a parallelogram. |

**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.

## As you can tell there are 2 bases b1 and b2. If you look back at the formula used b1 and b2 are used to find the answer. You need to know those two heights to complete the formula |

## Practice Questions

## As you can tell, the base of this parallelogram is 10cm, while the height is 8cm. Since a Parallelogram is just like a rectangle, you could do base * height. So 10*8=80 The area is 80cm | ## As you can tell, there are two bases. One reads 15cm and the other reads 38cm. The picture above also tells you that the height is 12 cm. The equation lists that A=1/2(b1=b2)h All you have to do now is plug the numbers in. A=1/2(b1+b2)h A=1/2(15+38)12 A=1/2*53*12 A=1/2*636 A=318cm squared |

## As you can tell, the base of this parallelogram is 10cm, while the height is 8cm. Since a Parallelogram is just like a rectangle, you could do base * height. So 10*8=80 The area is 80cm

## Chapter:10 Section:2

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

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.

## Practice Questions

## All you need to know for this equation is the radius. By looking at this picture the radius is 5 units. You now have to plug in the numbers into the equation like this: A=π*r2 A=π*5squared A=about 78.5 units |

## Chapter:10 Section:3

## 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.

## Practice Questions

## Chapter:10 Section:4

## Vocab seen in this section(:

**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

## Practice Questions

## This is a net and a 3d shape of a triangular prism. You need this net to help you figure out the surface area of the prism. The perimeter is "connecting" the three boxes on the top, the height is on the side, and the area of the base is going to be the area of the little triangles on the net. Once you figure all of those out, plug them into your formula. S=2B+Ph S=2*72+27*9 S=144+243 S=387cm cubed(3) | ## What you need to know to find out the surface area of a cylinder is the height and radius. As you can tell the radius is 5in and the height is 7in. Now you have to plug in the numbers. But know that there are smaller equations in between the formula. S=2B+Ch (the equation for the base of a cylinder is different, its π*r2. This also goes for the Circumfrance, the mini equation is 2*π*r) S=2*π*5 squared +2*π*5*7 S=157+219.8 S= about 376.8in squared |

## This is a net and a 3d shape of a triangular prism. You need this net to help you figure out the surface area of the prism. The perimeter is "connecting" the three boxes on the top, the height is on the side, and the area of the base is going to be the area of the little triangles on the net. Once you figure all of those out, plug them into your formula.

S=2*72+27*9

S=144+243

S=387cm cubed(3)

## What you need to know to find out the surface area of a cylinder is the height and radius. As you can tell the radius is 5in and the height is 7in. Now you have to plug in the numbers. But know that there are smaller equations in between the formula.

S=2*π*5 squared +2*π*5*7

S=157+219.8

S= about 376.8in squared

## Chapter:10 Section:5

## 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*

*l*). The formula for the surface area of a cone is S=π*r2+π*r*

*l*

## Practice Questions

## As you can tell, the height is 15in, the slant height is 17in and the base is 16 by 16 in. You now have to plug those into the formula. S= B+1/2*P* l
S=256+480 S=736 in squared | ## As you can tell the Slant height is 10cm, the height is 8.7cm, and the radius is 5cm. All you really need to do now is plug the numbers into the equation. S=π*r2+π*r* lS=π*25+π*5*10 S=78.5+157 S=235.5cm squared |

## As you can tell, the height is 15in, the slant height is 17in and the base is 16 by 16 in. You now have to plug those into the formula.

*l*

*S=256+*1/2*64*15

S=256+480

S=736 in squared

## Chapter:10 Section:6

## 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

## Finding the volume of a prism is very easy. All you have to do is find the area of the base and the height. You can both tell those two measurements by looking at the picture. V=B*h V=192*6 V=1152 cm cubed(3) | ## All you need to complete this formula is the area of the base and the height. But to find the area of the base, you have to do π*r2 since its a cylinder. It is now time t plug the numbers into the formula. V=B*h V=28.26*10 V=282.6cm cubed (3) |

## Finding the volume of a prism is very easy. All you have to do is find the area of the base and the height. You can both tell those two measurements by looking at the picture.

V=192*6

V=1152 cm cubed(3)

## Chapter:10 Section:7

## 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

## Practice Questions

## Extension of Chapter 10-7

## 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

## Practice Questions

## 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.