Chapter 10
Grant F
10.1- Area=^2 : Volume=^3: LABELS: cm,m,ft,in
Areas of parallelograms
Height- is a measure of a polygon or solid figure, taken as a perpendicular from the base of the figure and trapezoids
Base- or radix is the number of different digits that a system of counting uses to represent numbers
Parallelogram
The area of the parallelogram is the the product of the base and the height
A=b*h
Trapazoid
A= 1/2*(b1+b2)*h
*The area of the trapezoid is one half the product of the sum of the bases and the height
A= 1/2*(b1+b2)*h
.5 * 6 * (6+1)
3*7
21
Vocabulary
Base of a parallelogram- The length of anyone of its sides.
Height of a parallelogram-The perpendicular distance between the base and the opposite side
Base of a Trapezoid- 2 parallel sides
Height of a trapezoid- The perpendicular distance between the bases
10.2
Area of a circle
A=pi(3.14)*r2
pi times radius squared
Circle
circumference-2*pi*r
A=(Pi/4)*D
*The area is the product of pi and the square of the radius
Example-
A=pi * r^2 d= 10
3.14 * 5^2
78.5
Vocabulary
Area-The surface of amount of material needed to cover the shape
circle- radius, diameter, circumference
pi-3.14 or 22/7 pi=3.14159265359
10.3
Prism- 2 congruent bases that lie in parallel planes. another sides are rectangles
Pyramid-1base. all the other sides are triangles.
cylinder, cone, sphere
cylinder-a solid with 2 congruent circular bases that connect with parallel lines.
cone- a solid with 1 circular base
sphere-solid formed by all points in space that are same distance from one point called center
vertices, faces, edges
vertices-each angular point of a polygon, polyhedron, or other figure/3 or more edges meet
faces- surfaces of a solid objects
Edges- where 2 surfaces meet
F+V=E+2d
kinds of solids
prism-rectangular prism
pyramid- rectangular pyramid
cylinder-solid with 2 congruent circular bases that are parallel
cone, -1 solid with one circular base
sphere
Polyhedron-a solid that is enclosed by polygons
POLYGONS-a plane figure with at least three straight sides and angles, and typically five or more.
^
10.4
Surface area of a Prism
S=2B+Ph
The Surface area of a prism is the sum of twice the area of the base(B) and the product of the bases perimeter P and the height h.
S=2B+Ph
2(1/2*10*12)+(13+13+10)*15
=660
Surface area of a cylinder
The surface area of a cylinder id the sum of twice the area of a base B and the product of the bases circumference C and the height h.
Vocabualry and extra
Net-a two dimensional pattern that forms a solid when it is folded
Surface area-The sum of the areas of its faces
Triangular prism- find the sum of the areas of the two triangular faces and the 3 rectangular faces.
10.5
Surface areas of pyramids and cones
Surface area=Area of base+Number of triangles*area of each triangle
surface area of a pyramid
S=B=+1/2*P*l
surface area of a cone
S=pi*r^2+pi*r*l
extra
S=B+1/2Pl
S=27.7+1/2[24][6]
99.7
S=pi r2+ pirl
Pi[4]2+4*9
163.4
10.6
volume-the amount of space that a substance or object occupies, or that is enclosed within a container, especially when great
Volume of a prism
Volume is the area of the base and the height
Volume of a cylinder
V=Bh
volume = π · r^2 · h
The volume is the product of the area of the base times the height
π*4^2*6
301.593
extra
B=area of the base
P= perimeter of the base
10.7
Volumes of pyramids and cones
Cone and cylinder
The volume of a cone is related to volume of a cylinder. The cone is one third the volume of a cylinder with same base and height
Same thing with prisms and pyramids
Volume of a cone
V=1/3Bh
V=1/3*pi*r^2*h
Volume equals one third area of the base and the height
Volume of a pyrimid
V=1/3*B*h
Volume is one third, area of the base and the height
Sphere
V=^3
A=^2
Volume
V=4/3*pi*r^3
Volume is four thirds, pi, and radius cubed
surface area
SA=4*π*r^2
Sphere
Sphere
Volume
Surface area
Formulas
Trapezoid area-A=1/2(b1+b2)h
Circle area-A=pi*r^2
Surface area of prism-SA=2B +Ph
Surface area of a cylinder-SA=2B+Ch : SA= 2*pi*r^2+2*pi*r*h
Surface area of a pyramid-SA=B+1/2Pl
Surface area of a cone-SA=Pi*r^2+pi*r*l
Volume of a prism-V=Bh
Volume of a cylinder-V=Bh : V=Pi*r^2*h
Volume of a pyramid-V=1/3*B*h
Volume of a cone-V=1/3*B*h : V=1/3*pi*r^2*h
Volume of a sphere-V=4/3*pi*r^3
Surface area of a sphere-SA=4*pi*r^2
Real life
Real life
Pythagorean Theorem
a^2+b^2=c^2