Chapter 10
Paytyn M
10.1
~base of a parallelogram- the length of any one if its sides.
~height of a parallelogram- the perpendicular distance between the base and the opposite side
~bases of a trapezoid-its two parallel sides
~height of a trapezoid-the perpendicular distance between the bases
Finding Area of a Parallelogram and Trapezoid
A=bh write formula for area of a parallelogram
=8*10 Substitute 8 for b and 10 for h
=80 multiply
{80 inches squared is the answer}
Trapezoid:
A=1/2(b1+b2)h Write formulas for area of a trapezoid
=1/2(31+77)25 Substitute values for b1, b2 and h
=1350 multiply
{1350 square feet in the answer}
Real Life Examples
10.2
~area- the amount of surface the figure covers
~circle-is 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-the quotient of a circles circumference and its diameter
(3.14159)
Finding the Area of a Circle
= 3.14(5)2(squared) Substitute 3.14 for π and 5 for r (only use 3.14 when it says to)
=78.5 evaluate using a calculator
{Area is 78.5 square inches}
Real Life Examples
10.3
~solid-a three-dimensional figure that encloses a part of a space
~polyhedron-a solid that is enclosed by polygons
~face-the polygons that form a polyhedron
~prism- a polyhedron. Have 2 congruent bases that lie in parallel planes, other faces are rectangles.
~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 that are the same distance from a fixed point called the center
~edge-the segments where faces of a polyhedron meet
~vertex-a point where three or more edges meet
Classifying Three-Dimensional Figures
Polyhedron-a solid that is enclosed by polygons
Chart
10.4
~net- a two-dimensional pattern that forms a solid when it is folded
~surface area-(of a polyhedron)the sum of the areas of its faces
Finding the Surface Area of Prisms and Cylinders
S=2B+Ph Write formula for surface area of a prism
=2(1/2*10*12)+(13+13+10)*15 Input the values for the variables
=660 Solve
{660 square centimeters}
Cylinder:
S=2πr2 +2πrh Write formula for surface area
=2π(4)2(squared)+2π(4)*(10.7) Substitute 4 for r and 10.7 for h
=369.45 Evaluate using a calculator
{surface area is 369.45 square centimeters}
Real Life Examples
10.5
~slant height-(l of a regular pyramid) the height of a lateral face, that is, any face that is not the base
Finding the Surface Area of Pyramids and Cones
Pyramid:
=27.7+1/2*(24)*(6) Substitute 27.7 for B, 24 for P, and 6 for l
=99.7 Simplify
{Surface area of a pyramid is 99.7}
Cones:
S=πr2 +πrl Write Formula for surface area of a cone
=π(4)2 +π(4)*(9) Substitute 4 for r and 9 for l
=163.3 Evaluate using a calculator
{ surface area is 163.4 square meters}
Real Life Examples
10.6
~volume-a measure of the amount of space a solid occupies
Finding the Volume of Prisms and Cylinder
Rectangle-
V=Bh Write formula for the volume of prism
=(l*w)*h write the formula for the area of the base
=12*(8)*(2) input the values for the variables
=192 Evaluate
{192 cubic inches}
Triangle-
V=Bh write formula for volume of a prism
=1/2*(4)*(3)*(10) write the formula for the area of a prism and input the values of the variables
=60 solve
{60 cubic meter}
Cylinder:
V=Bh write the formula for volume
=πr2h write formula for volume of a cylinder
=π*(3)2(squared)*(9) substitute 3 for and 9 for h
=81π simplify
=254.469 Evaluate with a calculator
{254.469 cubic centimeters}
Real Life Examples
10.7
~pyramid- 10.3
~cone- 10.3
~volume-10.6
Finding the Volume of Pyramids and Cones
V=1/3Bh Write formula for volume of a pyramid
=1/3 *(30 squared)*(14) Substitute 30 squared for b and 15 for h
=4500 Evaluate
{4500 cubic feet}
Cone:
V=Bh write formula for volume
=1/3πr2h write formula for volume of a cone
=1/3π*(6)squared*(12)
=144π simplify
=452.389 Evaluate
{About 452 cubic feet}
Real Life Examples
Finding the Volume and Surface Area for a Sphere
Formulas
Area of a trapezoid- A=1/2(b1+b2)h: b1 and b2 are the 2 bases of the trapezoid
Area of a circle-A=πr2( pie r-squared)
Surface area of a prism- S=2B+Ph(B is area of the base and P is the perimeter)
Surface area of a cylinder-S=2B+Ch=2πr2(r-squared) +2πrh (C= circumference of the base)
Surface Area of a Pyramid-S=B+1/2Pl
Volume of a Prism-V=Bh
Volume of a Cylinder-V=Bh =πr2(r-squared)h
Volume of a Pyramid-V=1/3Bh
Volume of a Cone-V=1/3Bh=1/3πr2(r-squared)h
Volume of a Sphere-V=4/3πr3(r-cubed)