chapter 10
Brook B
10.1- Area of a Parallelogram and trapezoid
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
Trapezoid: real life example
Parallelogram: real life example
Circle: Real life example
10.2 Areas of Circles
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
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
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
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
10.7 Volumes of Pyramids and cones
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
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
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