Chapter 10
Sam H.
Chapter 10 Formula Page
Area of Trapezoid~ A=.5(b1 + b2) h
Area of a Circle~ A= 3.14 r^2
Surface Area of a Prism~ S= 2B+Ph
Surface Area of a Cylinder~ S=2B+Ch= 2*3.14*r^2+2*3.14*r*h
Surface Area of a Pyramid~ S=B+.5*P*l
Surface Area of a Cone~ S=3.14*r^2+3.14*r*l
Volume of a Prism~ V=Bh
Volume of a Cylinder~ V=Bh=3.14*r^2*h
Volume of a Pyramid~ V= 1/3*B*h
Volume of a Cone~ V=1/3Bh=1/3*3.14*r^2*h
Volume of a Sphere~ V= 4/3*3.14*r^3
10.1 Vocabulary
Height of Parallelogram- The perpendicular distance between the base and the opposite side
Base of Trapezoid- The trapezoids two parallel sides
Height of Trapezoid- The perpendicular distance between the bases
10.1 Formulas
Area of Trapezoid~ A=.5(b1 + b2) h
10.1 Practice Problems
A=bh Write formula for area
=8*10 Substitute 8 for b and 10 for h
=80 Multiply
The parallelogram has an area of 80 square inches
10.2 Vocabulary
Radius- The distance between the center and any point on the circle
Diameter- The distance across the circle through the center
Circumference- The distance around a circle
Circle- The set of all points in a plane that are the same distance, called the radius, from a fixed point, called the center
Pi- The ratio of the circumference of a circle to its diameter
10.2 Formulas
10.2 Practice Problems
A= 3.14*r^2 Write formula for area
=3.14(5)^2 Substitute 3.14 for pi and 5 for r
=78.5 Evaluate using a calculator
The area is about 78.5 square inches
10.3 Vocabulary
Polyhedron- A solid that is enclosed by polygons
Face- The polygons that form a polyhedron
Prism- A polyhedron. Prisms have two congruent bases that lie in parallel planes. The other faces are rectangles. A cube is a prism with six square faces
Pyramid- A polyhedron. Pyramids have 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- Segments where faces of a polyhedron meet
Vertex- A point where three or more edges meet
10.3 Formulas
10.3 Practice Problems
Faces: 6
Vertices:6
10.3 Real Life Tie
10.4 Vocabulary
Surface Area- The sum of the areas of its faces on a polyhedron
10.4 Formulas
Surface Area of a Prism~ S= 2B+Ph
Surface Area of a Cylinder~ S=2B+Ch= 2*3.14*r^2+2*3.14*r*h
10.4 Practice Problems
S= 2B + Ph
=2(1/2*10*12) + (13 + 13 + 10)15
=660
The surface area of the prism is 660 square centimeters
10.5 Vocabulary
10.5 Formulas
Surface Area of a Pyramid~ S=B+.5*P*l
Surface Area of a Cone~ S=3.14*r^2+3.14*r*l
10.5 Practice Problems
Step 1~ Find perimeter of the base
P= 8 + 8 + 8= 24
Step 2~ Substitute into the formula for surface area
S=B+ 1/2Pl Write formula for surface area of pyramid
= 27.7 + 1/2(24)(6) Substitute 27.7 for B, 24 for P, and 6 for 1
=99.7 Simplify
The surface area is about 99.7 square meters
10.5 Real Life Tie
This could be helpful if you wanted to try out soccer or just get a new ball and you needed to get the correct size.
10.5 Real Life Tie
There that was easy now you know you can get a medium size cone!
10.6 Vocabulary
10.6 Formulas
Volume of a Prism~ V=Bh
Volume of a Cylinder~ V=Bh=3.14*r^2*h
10.6 Practice Problems
V= Bh
=lwh
=12(8)(2)
=192
The volume is 192 cubic inches
10.6 Practice Problems continued...
V=bh
=1/2(4)(3)(10)
=60
The volume is 60 cubic meters
10.7 Formulas
Volume of a Cone~ V=1/3Bh=1/3*3.14*r^2*h
10.7 Practice Problems
V= 1/3Bh Write formula for volume of pyramid
=1/3(30^2)(15) Substitute 30^2 for b and 15 for h
=4500 Evaluate using a calculator
The pyramid has a volume of 4500 cubic feet
Extra Formulas
Extra Practice Problems
V=4/3*3.14*r^3 Write formula for volume of a sphere
=4/3*3.14*(5)^3 Substitute 5 for r
=523.6 Evaluate using a calculator
The volume of the sphere is about 523.6 cubic inches