# Chapter 10

## Formulas

Section 10-1-------area of parallelagrams and trapozoids

A=bh

A=1/2 (b1+b2)h

Section 10-2----------area of circles

A=3.14 r*r

Section 10-4----------Surface area of prisms and cylinders

S=2B=P

S=2B+Ch

Section 10-5------Surface area of pyramids and cones

S=B+1/2 Pl

S=3.14 r*r + 3.14 rl

Section 10-6-------------volumes of prisms and cylinders

V=Bh

Section 10-7-----------volumes of pyramids and cones

V=1/3 B h

Extension-----Volume of a sphere

V=4/3 3.14 r*r*r

Extension-------surface area of a sphere

S=4*3.14 r*r

## Section 10-1-----------------area of parallelagrams and trapozoids

Area of a parallelagram

A=bh

=(6)(3)

=18

A=18 cm. sqrd.

Area of a trapazoid

A=1/2(b1+b2)h

=1/2 (16+10)7

=1/2(26)7

=1/2(182)

=91

A=91

The height (h) of any shape must be connected to a 90 degree angle

## Section 10-2----------area of circles

area of a circle

A=3.14*r*r

=3.14*5*5

=78.5

If you are not given the radius you must divide the diameter by 2

Finding radius, diameter, circumference and area of circles (HD)

## Section 10-4----------Surface area of prisms and cylinders

Surface area of a prism

S=2B+Ph

=2(3*4*1/2)+(3+4+5)(7)

=12+(3+4+5)(7)

=12+12(7)

=168

S-surface area

P-perimeter of the base

h-height

B-area of base

Surface area of a cylinder

S=2(3.14)r*r+2(3.14)rh

=2 (3.14) (4) (4) + 2 (3.14) (4) (10.7)

S=369

You can use the formula to find the surface area of the NET

## Section 10-5------Surface area of pyramids and cones

surface area of a pyramid

S=B + 1/2 P l l=slant height

= (4*5) 1/2 (5*2+4*2) 8

= (20) 1/2 (18) 8

S=1440

surface area of a cone

S=3.14*r*r +3.14*r*l

=3.14(4)(4)+3.14(4)(9)

=163.4

Real life tie in

If you want to make a party hat that is shaped like a cone you must find the surface area to find if it will fit your head or not.

## Section 10-6-------------volumes of prisms and cylinders

volume of a prism

V=Bh

=(5)(4)(7)

=140

Volume of a cylinder

V=Bh

=3.14 r*r h

## Section 10-7-----------volumes of pyramids and cones

For a good way to learn how to find the volumes watch this video
Volume of Cones and Pyramids 128-4.14

## Vocabulary

Area- The amount of surface a figure covers

Diameter- The distance from one end to the other on a circle

Circumference- The circular line on a shape

Net- The flattened pattern that forms a 3-D object when folded

Surface area- The sum of all the faces

Slant height- The height of the lateral face that isn't the base

Volume- The measurement of space an object takes up