# Chapter 10

## Chapter 10 Formula Page

Area of Parallelogram~ A=bh

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

Base of Parallelogram- The length of any of its sides

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

Area of Parallelogram~ A=bh

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

Area- The number of square units covered by a figure

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

Area of a Circle~ A= 3.14 r^2

## 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

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

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

Euler's Formula~ E+2= F+V

Edges: 10

Faces: 6

Vertices:6

## 10.3 Real Life Tie

Right when you wake up in the morning you are starving and you can only think of one thing your favorite cereal lucky charms! While pouring your cereal in the bowl you look at the box and wonder how it was made. Huh i wonder how you find the edges, vertices, and faces? Well its easy as long as you know the definitions. Just count them up!

## 10.4 Vocabulary

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

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

Surface Area of a Cylinder 128-4.11

## 10.5 Vocabulary

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

## 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

How To Find The Total Surface Area Of A Cone: THE EASY WAY!

## 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

In order to find the surface area of a soccer ball you would need to understand section 10.5 from this unit. The formula you would use would be S=4*3.14*r^2

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

So are you in the mood for a nice ice cream cone? I sure am. Then you realize you only have 2.00 dollars so you are not sure what size you can get. Well its easy if you know how to find the surface area of a cone! The formula is S= 3.14* r^2 + 3.14*r*l

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

## 10.6 Vocabulary

Volume of Solid- A measure of the amount of space it occupies, measured in cubic units

## 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

Volume of a Prism - MathHelp.com - Math Help

## 10.7 Formulas

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

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

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

## 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

3D Shapes I Know (solid shapes song- including sphere, cylinder, cube, cone, and pyramid)