# Chapter 10

## **Don't Forget**

Labels--in^2, m^3, etc.

## Area

• Parallelogram/Rectangle : b*h
• Trapezoid : 1/2(b1+b2)h
• Circle : Pi*r^2
• Triangle : 1/2*b*h
• ## Surface Area

• Cylinders : 2B+Ch or 2Pir^2+2Pirh
• Prisms : 2B+Ph
• Pyramid : B+1/2*P*l

• Cone : Pi*r^2+Pi*r*l

• Sphere: S=4*pi*r^2

• ## Volume

• Cylinders : 2B+Ch or 2Pir^2+2Pirh
• Prisms : 2B+Ph
• Pyramid : B+1/2*P*l

• Cone: Pi*r^2+Pi*r*l

• Sphere: V=4/3*pi*r^3

• ## Extra

Slant Height: l=square root of (r^2+h^2)

-E+2=F+V (find out if edges, vertices, and faces are correct on a 3-dimensional object)

Notes:

-capital letters in formulas are usually associated with area

## Vocabulary

• The base if a parallelogram is the length of any one of its sides
• The height of a parallelogram is the perpendicular distance between the base and the opposite side.
• The base of a trapezoid are its two parallel sides
• The height of a trapezoid is the perpendicular distance between the bases

## Paralellograms

• The area of a parallelogram is the product of the base and the height.
• The formula for a parallelogram is A=bh.
• The b stands for the base, the length of any one of its sides.
• The h is the height, and is always perpendicular to the base.

## Trapezoids

• The area of a trapezoid is one half the product of the sum of the bases and the height.
• The formula is A=1/2(b1+b2)h.
• b1 stands for the 1st base.
• b2 is the 2nd base.
• The h is always perpendicular to b1 and b2.
• The bases are parallel.

## Practice Problems

Parallelogram:

h=3cm b=5cm
A=b*h

A=5*3
A=15cm squared

Trapezoids:

b1=2mm b2=4mm h=5mm

A=1/2(b1+b2)h

A=1/2(2+4)5

A=1/2*30

A=15mm

Real Life:
The Winslow House in River Forest, Illinois, was designed by Frank Lloyd Wright. The front part of the roof is a trapezoid. What is the area is b1=31ft b2=77ft and h=25ft?

## 10.2: Areas of circles

Formula:
Area of a circle: A=pi*r2

Vocab:
A circle is the set of all points in a plane that are the same distance from a fixed point

Practice:
Circle
r=5
A=pi*5squared
A=78.53981634...

Real Life:
Todd puts in a hot tub in his back yard. He needs to figure out how much space it will take up. The diameter is 3ft. Find the area.

Answer: 7.068583471ft... or 8ft

## 10.3 Three-Dimensional Figures

Formulas:

-E+2=F+V (find out if edges, vertices, and faces are correct on a 3-dimensional object)

-E= edges

-F= faces

-V= vertices

Vocabulary:

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

Polyhedron: A solid that is enclosed by polygons.

Prism: A polyhedron, has two congruent .bases that lie in parallel planes. The other faces are rectangles.

Pyramid: Is a polyhedron, has one base, and 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: The segments where faces of a polyhedron meet.

Vertex: A point where three or more edges meet. (Plural of vertex is vertices.)

Notes:

-solid shape (prism, pyramid) is defined by its base

ex: rectangular prism, rectangular pyramid

-lateral area is the area of the sides (everything but the base/bases)

## 10.4 Surface Area of prisms and Cylinders

Formula:
Surface area of a prism: S=2B+Ph
Surface area of a cylinder: 2B+Ch or 2*pi*r2 + 2*pi*r*h
Lateral surface area= 2*pi*r*h

Vocab:
(S) is surface area
(2B) is the sum of twice the area of the base
(Ph) is the product of the base's perimeter and the height
(Ch) is the product of the base's circumference and the height
A prism is a polyhedron that have two congruent bases that lie in parallel planes and the other faces are rectangles.
A cylinder is a solid with two congruent circular bases that lie in parallel planes

Practice:
Triangular Prism
B=.5*10*12cm
P=13+13+10cm
h=15cm
A+2(.5*10*12) + (13+13+10)15
A=660cm

## 10.5 Surface area of Pyramids and Cones

Formula:
Surface area of a pyramid: S=B+.5*Pl
Surface area of a cone: S=pi*r2* + pi*r*l
Curved lateral surface of a cone: A= pi*r*l

Vocab:
slant height of a regular pyramid is the height of a lateral face, that is, any face that is not the base
(.5Pl) is one half of the product of the base perimeter and the slant height

Practice:
rectangular pyramid
B=27.7
P=24
l=6
S=B+.5*Pl
S=27.7+.5(24)(6)

Real Life!

Bob works at an ice cream shop. He decided to some extra chocolate to dip a cone in. Bob's not sure if he has enough chocolate so he want's to calculate the surface area of the cone. If the radius is 2in and the slant height is 4in, then what is the surface area?

Answer:37.69911184in squared or 37in squared

## 10.6 Volumes of Prisms and Cylinders

Formula:
Volume of a Prism: V=B*h
Volume of a Cylinder: V=B*h or V=pi*r2*h

Vocab:
The volume of a solid is a measure of the amount of space it occupies.

Practice:
prism
l=12
w=8
h=2
V=B*h
V=12(8)(2)
V=192

## 10.7 Volume of Pyramids and Cones

Formula:
Volume of a Pyramid: V= 1/3*B*h
Volume of a cone: V=1/3*B*h or V=1/3*pi*r2*h

Vocab:
Pyramids are polyhedrons that have one base. The other faces are triangles
A cone is a solid with one circular base

Practice:
pyramid
B=30squared
h=15
V=1/3*B*h
V=1/3(30squared)(15)
=4500

## Surface area of a Prism

How To Get The Surface Area Of A Triangular Prism

## Pyramids

Geometry - Finding the volume and surface area of a pyramid with a rectangular base - Cool Math

## Cones

Volume and Surface Area of Cones