Chapter 10
Sam P
All formulas in Chapter 10
Area of trapezoid: A=1/2(b1+b2)h
Area of circle: A=πr²
Surface area of a prism: S=2B+Ph
Surface area of a cylinder: S=2B+Ch
Lateral area of a cylinder: S=2πrh
Surface area of a pyramid: S=B+1/2*Pl
Surface area of a cone: S=πr²+πrl
Lateral area of a cone: S=πrl
Surface area of a sphere: S=4πr²
Volume of a prism: V=Bh
Volume of a cylinder: V=Bh
Volume of a pyramid: V=1/3*Bh
Volume of a cone: V=1/3*Bh
Volume of a sphere: V=4/3πr³
10.1
Area of parallelograms and trapezoids
Vocabulary
~Base of a parallelogram- The length of any one of a parallelogram's sides..
~Height of a parallelogram- The perpendicular distance between the base and the opposite side.
~Bases of a trapezoid- The two parallel sides.
~Height of a trapezoid- The perpendicular distance the two bases.
Formulas:
Parallelogram: A=bh
Trapezoid: A=(b1+b2)h
**b1= base one, b2= base two, h= height**
Practice problems
Real life example
You are re-roofing your house the roof is in the shape of a trapezoid, and you need to know how many squares of shingles you need. You can use the formula for area of a trapezoid to find just the right amount of shingles. (Ex. b1= 30ft, b2= 35ft, h=15ft.)
10.2
Area of circles
Vocabulary
~Area- The amount of surface the figure covers.
~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 the circle.
~Diameter- The distance across the circle through the center, or twice the radius.
~Circumference- The distance around the circle.
~Pi- A non- terminating decimal that with any circle it is the circumference divided by its diameter.
Formulas:
A=πr²
**A= Area, r= radius**
Practice problems (use 3.14 for pi and round to nearest hundreth)
#1
A=πr²
A=3.14*3²
A=3.14*9
A=28.26cm²
#2
#3
Real life example
10.3
~Solid- A three-dimensional figure that encloses a part of space.
~Polyhedron- A solid that is encloses by polygons.
~Faces- The polygons that form a polyhedron.
~Prism- A polyhedron with two congruent bases that lie in parallel planes. The other faces are rectangles.
~Pyramid- A polyhedron with one base. The 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- Where faces of a polyhedron meet.
~Vertex- A point where three or more edges meet.
Practice problems- Classify the solid then tell whether it is a polyhedron
#1
#2
#3
10.4
Surface area of prisms and cylinders
Vocabulary
~Net- A two-dimensional pattern that when folded forms a solid.
~Surface area- The sum of the areas of a polyhedrons faces.
~Lateral surface area- The surface area of a three-dimensional figure excluding the area of its bases.
Formulas:
Prism: S=2B+Ph
Cylinder: S=2B+Ch
S=2πr²+2πrh
lateral area of cylinder: 2πrh
**S=Surface area, B= Area of the objects base, P= Perimeter of the base, h=height**
Practice problems- Find the surface area of the solid
#1
#2
#3
S=2*6*3*+18*4
S=36+72
S=108cm²
Real life example
10.5
Surface area of pyramids and cones
Vocabulary
~Slant height- The height of a lateral face, which is any face that is not a base.
Formulas:
Pyramid: S=B+1/2*Pl
Cone: S=πr²+πrl
Lateral surface area of a cone: S=πrl
**S= Surface area, B= Area of the objects base, P= perimeter of the base, l= slant height**
**r= radius, l= slant height**
Practice problems
#1
#2
S=1024+1/2*128*34
S=1024+1/2*4352
S=1024+2176
S=3200in²
#3
Real life example
10.6
Volume of prisms and cylinders
Vocabulary
~Volume- A measure of the amount of space it occupies.
Formulas:
Prism: V=Bh
Cylinder: V=Bh
V=πr²*h
**V= Volume, B= Area of base, h= height**
Practice problems- Find the volume of the solids
#1
#2
A=Bh
A=20*9*8
A=180*8
A=1440cm³
#3
Real life example
10.7
Volume of pyramids and cones
Vocabulary
~Pyramid- A polyhedron with one base. The other faces are triangles.
~Cone- A solid with one circular base.
~Volume- A measure of the amount of space it occupies.
Formulas:
Pyramid: V=1/3*Bh
Cone: V=1/3*Bh
V=1/3*πr²*h
**V= Volume, h= height**
Practice problems- Find the volume of the solids
#1
#2
#3
V=1/3*56*12
V=1/3*672
V=224cm³
Real life example
Sphere
Surface area and volume of spheres
Vocabulary
~Sphere- A solid formed by all points in space that are the same distance from a fixed point called the center.
~Volume- A measure of the amount of space it occupies.
Formulas:
S=4πr²
V=4/3*πr³
**S=Surface area, r= radius**
**V= Volume, r= radius**
Practice problems
#1 find the volume
#2 find the surface area
#3 find the volume
V=4/3*πr³
V=4/3*3.14*14³
V=4/3*3.14*2744
V=4/3*8616.16
V=11488.2cm³