# Chapter 10

## Vocab

section 1:

Base of a parallelogram-The length of any one of its sides

height of a parallelogram-The perpendicular distance between the base and opposite side

bases of a trapezoid-It's two parallel sides

height of a trapezoid-The perpendicular distance between the bases

Section 2:

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 a circle

diameter-The distance across the circle through the center

circumference-The distance around a circle

pi-3.14

Area-The amount of surface that a figure covers

Section 3:

solid-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 with rectangle faces and two bases

pyramid-Polyhedron with one base and triangular faces

cylinder-A solid with two congruent circular bases

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

Section 4

net-A two dimensional pattern that forms a solid when it is folded

surface area-The sum of the area of its faces

Section 5:

slant height-The height of a lateral face

Section 6:

Volume-A measure of the amount of space it occupies

## Section 1

Area of a Square: b*h=A

Area of trapezoid: 1/2*(b1+b2)*h=A

## Section 2

Area of circle: A= pi r2 (radius to the second power)

Circumference of a circle: C=2pi r

## Section 4

Surface area of a prism: S=2B+Ph

The surface area of a prism is the sum of twice the area of a base, B, and the product of the bases perimeter, p, and the height, h.

Surface area of a cylinder: S=2B+Ch=2pi r to the second power+2pi rh

B (pi r to the second power)

The surface area of a cylinder is the sum of twice the area of the base, B, and the product of the bases circumference, C, and the height, h.

## Section 5

Surface area of a pyramid: S=B+1/2Pl

The surface area of a pyramid is the sum of the area of the base and one half the product of the base perimeter,p and the slant height, l.

To find slant height, use Pythagorean theorem

Surface area of a cone: S=pi r to the second power+pi rl

The surface area of a cone is the sum of the area of the circular base with the radius, r, and the product of pi, the radius r of the base, and the slant height l.

## Section 6

Volume of a rectangular prism: V=B*h (l*w*h)

Volume of triangular prism: V=B*h (1/2*b*h)*h

Volume of Cylinder: V= B*h (pi*r to the second power*h)

## Section 7

Volume of a pyramid: V=1/3*B*h

Volume of Sphere: V=4/3 pi r to the 3rd power

Volume of a cone: V= 1/3 pi r to the second power h

## Practice Problems

Surface area of a pyramid:

B=64m

P=32m

l=7.2m

Volume of a cone:

height=7m

Volume of a triangular prism:

Height=12ft

Area of base=6.2ft

Area of a trapezoid:

base=12.3m

Height=7.5m

Surface area of a cylinder:

Diameter= 8cm

Height= 10.7cm

## Real life example

People who design a soup can need to know the surface area of the can.
Volume Of A Cylinder
Volume Of A Cone
Volume of a Sphere - MathHelp.com - Math Help
Surface Area of a Pyramid