# Chapter 10

## 10.1

Vocabulary:

~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

Parallelogram:

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}

## 10.2

Vocabulary:

~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

A=πr2 Write the formula for 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}

Area of a circle

## 10.3

Vocabulary:

~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

## 10.4

Vocabulary:

~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

Prism:

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}

## 10.5

Vocabulary:

~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:

S=B+1/2Pl Write formula for surface area of a 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}

## 10.6

Vocabulary:

~volume-a measure of the amount of space a solid occupies

## Finding the Volume of Prisms and Cylinder

Prism:

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}

Volume of a Triangular Prism

Vocabulary:

~pyramid- 10.3

~cone- 10.3

~volume-10.6

## Finding the Volume of Pyramids and Cones

Pyramid:

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

## Finding the Volume and Surface Area for a Sphere

Volume of a Sphere
Surface Area Of A Sphere

## Formulas

Area of a parallelogram- A=bh

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)