chapter 10

Brook B

10.1- Area of a Parallelogram and trapezoid

how to find the area of a parallelogram

a= bh

the area of a parallelogram is the product of the base and the height


Example:

A= b write formula for area

= 8(10) substitute 8 for b and 10 for h

=80 multiply


How to find the area of a trapezoid

a= 1/2(b1+b2)h

the area of a trapezoid is one half the product of the sum of the bases and the height.


example:

a=1/2(b1+b2)h write formula for area

=1/2(31+77)25 substitute values for b1,b2 and h

=1350 multiply

10.2 Areas of Circles

How to find the area of a circle

a=(pi)r^2

the area of a circle is the product of pi and the square root of the radius


example:

a=(pi)r^2 write the formula

=3.14(5)^2 substitute 3.14 for pi and 5 for r

=78.5 evaluate using a calculate

10.3 Three-dimensional FIgures

10.3 Three-dimensional Figures


How to classify 3D figures



How to count the faces, edges, and vertices



How to draw prisms and other 3D figures

3D-Shapes: Vertices, Edges and Faces

10.4 Surface areas of Prisms and Cylinders

How to Find the surface area of a prism

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.


S=2B+Ph


example:

S= 2B + Ph

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

=660



How to find the surface area of a cylinder

the surface area of a cylinder is the sum of twice the area of the base B and the product

of the base's circumference C and the height h


S=2B+Ch= 2(pi)r^2+2(pi)rh


Example:

S=2(pi)r^2+(pi)rh write formula

=2(pi)4^2=2(pi)4*10.7 substitute 4 for r and 10.7 for h

=369.45 evaluate using calculator

10.5 Surface areas of pyramids and cones

How to find the surface area of a pyramid

The surface area of a regular pyramid is the sum of the area of the base B and one half the product of the base perimeter P and the slant height l


S= B+1/2*Pl


example:

B=27.7 find the area of the base

P=8+8+8=24 find the perimeter of the base (add up all the sides)

S=B+1/2Pl write the formula for the surface area of a pyramid

=27.7+1/2*24*6 substitute

=99.7 simplify


How to find the surface of a cone

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


S=(pi)r^2+(pi)rl


example:

S= (pi)r^2= (pi)rl write formula for surface area of cone

= (pi)4^2+(pi)4*6 substitute 4 for r and 9 for l

=163.4 evaluate using calculator

10.6 volumes of prisms and cylinders

How to find the volume of a prism

the volume of a prism is the product of the area of the base B and the height h

V=Bh


example:

rectangular base

V=Bh

=lwh

=12*8*2

=192


triangular base

v=Bh

=1/2*4*3*10

=60


How to find the volume of a cylinder

The volume of a cylinder is the product of the area of a base B an d the height h

v=Bh

=(pi)r^2h


Example:

v=Bh write formula for volume

=(pi)r^2h write formula for a volume of a cylinder

=(Pi)3^2*9 substitute

=81(pi) simplify

=254.469 evaluate using a calculator

How vegetables are canned

real life tie In: when you are creating the cans you must find and incorporate the volume of the cans for packaging and creating the can itself.
Canned vegetables Process

10.7 Volumes of Pyramids and cones

How to find the volume of a Pyramid

The volume V of a Pyramid is one third the product of the area of the base Base and the height h


V=1/3 Bh


example:

V=1/3Bh write the formula

=1/3*30^2*15 substitute for B and h

=4500 evaluate using a calculator


How to find the volume of a cone

The volume of a cone V is one third the product of the area of the base B and the height h

v==1/3*Bh=1/3

(pi)r^2h


example:

V=1/3(pi)r^2 write the formula

=1/3(pi)*6^2*12 substitute for r and h

=144(pi) simplify

=452.389 evaluate using calculator

Formulas

10.1

area of a parallelogram: a=bh

area of a trapezoid: a=1/2(b1+b2)h

10.2

area of a circle: a=(pi)r^2

10.4

surface area of a prism: SA= 2B+Ph

surface area of a cylinder: SA=2B+Ch= 2(pi)r^2+2(pi)rh

10.5

surface area of a pyramid: SA= B+1/2*Pl

surface area of a cone: SA=(pi)r^2+(pi)rl

10.6

volume of a prism and a cylinder: V=Bh

rectangular prism B=lwh

Cylinder B=(pi)r^2

10.7

volume of a pyramid: V= 1/3Bh

volume of a cone: v==1/3*Bh=1/3

b= (pi)r^2h

vocabulary

10.1

base of a parallelogram: is the length of any one of its sides.

Height of a parallelogram: the perpendicular distance between the base and the opposite side

base of a trapezoid: are its two parallel sides

height of a trapezoid: perpendicular distance between the bases

10.3

soild: is a three-dimensional figure that encloses a part of space

polyhedron: is a solid that is enclosed by polygons

Faces: the polygons that form a polyhedron