# Chapter 10

### Sam H.

## Chapter 10 Formula Page

**A=bh**

*Area of Parallelogram~***Area of Trapezoid~** A=.5(b1 + b2) h

**Area of a Circle~** A= 3.14 r^2

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

**Surface Area of a Cylinder~** S=2B+Ch= 2*3.14*r^2+2*3.14*r*h

**Surface Area of a Pyramid~** S=B+.5*P*l

**Surface Area of a Cone~ **S=3.14*r^2+3.14*r*l

**Volume of a Prism~ **V=Bh

**Volume of a Cylinder~** V=Bh=3.14*r^2*h

**Volume of a Pyramid~ **V= 1/3*B*h

**Volume of a Cone~ **V=1/3Bh=1/3*3.14*r^2*h

**Volume of a Sphere~** V= 4/3*3.14*r^3

## 10.1 Vocabulary

**The length of any of its sides**

__Base of Parallelogram-__**Height of Parallelogram-** The perpendicular distance between the base and the opposite side

**Base of Trapezoid-** The trapezoids two parallel sides

**Height of Trapezoid-** The perpendicular distance between the bases

## 10.1 Formulas

**A=bh**

__Area of Parallelogram~__**Area of Trapezoid~** A=.5(b1 + b2) h

## 10.1 Practice Problems

**Find the area of the parallelogram!**A=bh __Write formula for area__

=8*10 __Substitute 8 for b and 10 for h__

=80 __Multiply__

__The parallelogram has an area of 80 square inches __

## 10.2 Vocabulary

**The number of square units covered by a figure**

__Area-__**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

**Circle- **The set of all points in a plane that are the same distance, called the radius, from a fixed point, called the center

**Pi- **The ratio of the circumference of a circle to its diameter

## 10.2 Formulas

**A= 3.14 r^2**

__Area of a Circle~__## 10.2 Practice Problems

__Find the area of a circle with a diameter of 10 inches__

A= 3.14*r^2 __Write formula for area__

=3.14(5)^2 __Substitute 3.14 for pi and 5 for r__

=78.5 __Evaluate using a calculator__

__The area is about 78.5 square inches__

## 10.3 Vocabulary

**A three-dimensional figure that encloses a part of space**

__Solid-__**Polyhedron-** A solid that is enclosed by polygons

**Face-** The polygons that form a polyhedron

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

**Pyramid-** 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 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-** Segments where faces of a polyhedron meet

**Vertex-** A point where three or more edges meet

## 10.3 Formulas

**E+2= F+V**

__Euler's Formula~__## 10.3 Practice Problems

Faces: 6

Vertices:6

## 10.3 Real Life Tie

## 10.4 Vocabulary

**A two-dimensional pattern that forms a solid when folded**

__Net-__**Surface Area-** The sum of the areas of its faces on a polyhedron

## 10.4 Formulas

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

**Surface Area of a Cylinder~** S=2B+Ch= 2*3.14*r^2+2*3.14*r*h

## 10.4 Practice Problems

__Find the surface area of the triangular pyramid__

S= 2B + Ph

=2(1/2*10*12) + (13 + 13 + 10)15

=660

__The surface area of the prism is 660 square centimeters__

## 10.5 Vocabulary

**On a regular pyramid is the height of the lateral face, that is any face that is not a base.**

__Slant Height-__## 10.5 Formulas

**Surface Area of a Pyramid~** S=B+.5*P*l

**Surface Area of a Cone~** S=3.14*r^2+3.14*r*l

## 10.5 Practice Problems

__Find the surface area of the regular pyramid. Round to nearest tenth.__

**Step 1~ **__Find perimeter of the base__

P= 8 + 8 + 8= 24

**Step 2~ **__Substitute into the formula for surface area__

S=B+ 1/2Pl __Write formula for surface area of pyramid__

= 27.7 + 1/2(24)(6) __Substitute 27.7 for B, 24 for P, and 6 for 1__

=99.7 __Simplify__

__The surface area is about 99.7 square meters__

## 10.5 Real Life Tie

This could be helpful if you wanted to try out soccer or just get a new ball and you needed to get the correct size.

## 10.5 Real Life Tie

There that was easy now you know you can get a medium size cone!

## 10.6 Vocabulary

**A measure of the amount of space it occupies, measured in cubic units**

__Volume of Solid-__## 10.6 Formulas

**Volume of a Prism~** V=Bh

**Volume of a Cylinder~** V=Bh=3.14*r^2*h

## 10.6 Practice Problems

__Find the volume of the prism__

V= Bh

=lwh

=12(8)(2)

=192

__The volume is 192 cubic inches__

## 10.6 Practice Problems continued...

__Base is a triangle with 1/2bh__

V=bh

=1/2(4)(3)(10)

=60

__The volume is 60 cubic meters__

## 10.7 Formulas

**V= 1/3*B*h**

__Volume of a Pyramid~____Volume of a Cone~__ V=1/3Bh=1/3*3.14*r^2*h

## 10.7 Practice Problems

__Find the volume of the square pyramid__

V= 1/3Bh __Write formula for volume of pyramid__

=1/3(30^2)(15) __Substitute 30^2 for b and 15 for h__

=4500 __Evaluate using a calculator__

__The pyramid has a volume of 4500 cubic feet __

## Extra Formulas

**V= 4/3*3.14*r^3**

__Volume of a Sphere~__## Extra Practice Problems

__Find the volume of a sphere with a radius of 5 inches__

V=4/3*3.14*r^3 __Write formula for volume of a sphere__

=4/3*3.14*(5)^3 __Substitute 5 for r__

=523.6 __Evaluate using a calculator __

__The volume of the sphere is about 523.6 cubic inches__