# Ch. 10

### by Nick Vicich

## Important Formulas

**WHEN DEALING W/ANYTHING 'SQUARED', REMEMBER TO USE THE 'SQUARED' SYMBOL!!!**

**Volume = 'CUBED'!!!**

**WHEN DEALING W/ANYTHING 'CUBED', REMEMBER TO USE THE 'CUBED' SYMBOL!!!**

**Section 1:**

**'Area of a Parallelogram'**- A = bh**'Area of a Trapezoid'**- A = 0.5(b1 +b2)h'

h = the distance between the 2 bases

**Section** **2: **

**'Area of a Circle' -**A = (Pi the symbol)r*2 (*Pi r squared)

**Section** **3: **none

**Chapter 4: **

**'Surface Area of a Prism' -**S = 2B + Ph

B = area of the base (base * height)

P = the base's perimeter

h = is the distance between the 2 bases

2. **'Surface Area of a Cylinder' - **S =** **2B +Ch or** (in simpler terms)**

2(Pi symbol)r2 (r squared) + 2(Pi symbol)r*h

Section **5: **

**'Surface Area of a Pyramid' -**S = B + 0.5Pl

B = area of the base (0.5 * base * height)

P = the base's perimeter

l = slant height

** **2. **'Surface Area of a Cone' - **S = (Pi symbol)r2 (r squared) + (Pi symbol)r*l

l = slant height

Section **6: **

**'Volume of a Prism' -**V = Bh

B = area of the base (b*h)

h = the distance between the 2 bases

** **2. **'Volume of a Cylinder' - ** V = Bh

= (Pi symbol)*r2 (r squared)*h

B = the area of the base

h = is the distance between the 2 bases

Section **7: **

**'Volume of a Pyramid' -**V = 1/3Bh

h = is the distance between the 2 bases

## ch. 10 sec. 1 - areas of parallelograms and trapezoids

## Section 1 Vocab.

**Base of a parallelogram**- the length of any one 1 of its sides.**Height of a parallelogram**- the perpendicular distance between the base and the opposite side.**Bases of a trapezoid**- 2 parallel sides.**Height of trapezoid**- the perpendicular distance between the bases.

## Formula to finding the 'area of a Trapezoid'Here's your algebra:
Area=0.5(base #1 + base #2)height | ## Formula to finding the 'area of a Parallelogram'Here's your algebra:
Area=base*height | ## How to find the 'Area of a Parallelogram' Do this: A=bh Area=base*height |

## How to find the 'area of a Trapezoid' | ## Additional info. | The bases of a trapezoid are its 2 parallel sides. The perpendicular distance between the bases is the height of a trapezoid. Bases 1 and 2 can form a parallelogram with height h and base b1 + b2. |

## ch. 10 sec. 2 - areas of circles

## Section 2 Vocab.

**Area**- the number of square units covered by a figure. Example: 7 units by 2 units, the Area = 14 square units (**REMEMBER TO USE TO 'SQUARED' SYMBOL!!!).****Circle**- the set of all points in a plane that are the same distance, called the radius, form a fixed point, called the center.**Radius**- the distance between the center and any point on the circle.**Diameter**- the distance across the circle through the center.**Circumference**- the distance around a circle.**Pi**- the ratio of the circumference of a circle to its diameter. Example: you can use 3.14 or 22/7 to approximate Pi (like the symbol).

## A Good Ol' Quote From Mr. Chi'woo

**"Circles are bases, not faces!!"**

## ch. 10 sec. 3 - 3 dimensional figures

## section 3 vocab.

**Solid**- 3 dimensional figure that encloses a part of space. Example: a sugar cube.**Polyhedron**- a solid that's enclosed by polygons. A polyhedron**has only flat surfaces.****Face**- a polygon that is a side of the polyhedron.**Prism**- a solid,, that__formed by polygons____has 2 congruent bases lying in parallel planes.__**Pyramid**- a solid, formed by polygons, thatThe base can be any polygon, and the other faces are triangles.**has 1 base**.**Cylinder**- a solid with__2 congruent circular bases that lie in parallel planes.__**Cone**- a solid with__1 circular base.__**Sphere**- a solid__formed by all points in space that are the same distance from a fixed point called the center.__**Edge**- a line segment where__2 faces of the polyhedron meet.__**Vertex**- a point at which__3 or more edges of a polyhedron meet.__

## ch. 10 sec. 4 - Surface Areas of Prisms and Cylinders

## sec. 4 vocab.

**net**-**surface area**- the sum of the areas of the faces of the polyhedron.

The net of a cylinder has 2 circles for the bases. The curved surface of the cylinder becomes a rectangle in the net. The width of the rectangle is the height of the cylinder, and the length of the rectangle is the circumference of the base. | ## formula to finding the 'surface area of a cylinder' | ## how to find the 'surface area of a cylinder' |

## ch. 10 sec. 5 - surface areas of pyramids and cones

## Sec. 5 Vocab.

**Slant Height -**the height of any face that is not the base of a regular pyramid

## Using the net of a pyramid to find the surface area of the pyrmid | ## formula to finding the 'surface area of a pyramid' | ## how to find the 'surface area of a pyramid' |

## Ch. 10 sec. 6 - volumes of prisms and cylinders

## sec. 6 vocab.

**Volume -**the amount of space the solid occupies.

The vol. of a prism can be calculated by finding the # of square units in the base and multiplying by the height. The formula for the volume of a cylinder is similar to the formula for the volume of a prism. | ## Formula to finding the 'volume of a cylinder' | ## how to find the 'volume of a cylinder' |

## ch. 10 sec. 7 - volumes of pyramids and cones

## sec. 7 vocab.

**Pyramid -**a solid, formed by polygons, that has 1 base. The base can be any polygon, and the other faces are triangles.**Cone -**a solid with 1 circular base.**Volume -**the amount of space the solid occupies.

## Formula to finding the 'volume of a pyramid' | ## how to find the 'volume of a pyramid' | The volume of a cone is related to the volume of a cylinder in the same way the volumes of a pyramid and a prism are related. That is, the volume of a cone is 1/3 the volume of a cylinder with the same base and height. |