artysurface area & volume

7/28/2019 ArtySurface Area & Volume

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Geometry Formulas:

Surface Area

& Volume

ARTYCLASS -10B


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A formula is just a set of instructions.

It tells you exactly what to do!

All you have to do is look at the

picture and identify the parts.

Substitute numbers for the variables

and do the math. Thats it!


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Lets start in the beginning

Before you can do surface area or volume,

you have to know the following formulas.

Rectangle A = lwTriangle A = bh

Circle A = r

C = d


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You can tell the

base and height

of a triangle by

finding the

right angle:

TRIANGLES


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CIRCLES

You must know the difference

between RADIUS and DIAMETER.

r

d


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Lets start with a rectangular prism.

Surface area can be done using the formula

SA = 2 lw + 2 wl + 2 lw OR

Either method will gve you the same answer.

you can find the area

for each surface and

add them up.

Volume of a rectangular prism is V = lwh


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Example:

7 cm

4 cm

8 cm

Front/back 2(8)(4) = 64

Left/right 2(4)(7) = 56

Top/bottom 2(8)(7) = 112

Add them up!

SA = 232 cm

V = lwh

V = 8(4)(7)

V = 224 cm


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To find the surface

area of a triangular

prism you need to beable to imagine that

you can take the

prism apart like so:

Notice there are TWO congruent triangles

and THREE rectangles. The rectanglesmay or may not all be the same.

Find each area, then add.


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Example:

8mm

9mm

6 mm 6mm

Find the AREA of each SURFACE

1. Top or bottom triangle:

A = bh

A = (6)(6)

A = 18

2. The two dark sides are the same.

A = lw

A = 6(9)

A = 54

3. The back rectangleis different

A = lw

A = 8(9)

A = 72

ADD THEM ALL UP!

18 + 18 + 54 + 54 + 72

SA = 216 mm


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SURFACE AREA of a CYLINDER.

You can see that

the surface is

made up of two

circles and arectangle.

The length of the rectangle is the same as

the circumference of the circle!

Imagine that

you can open up

a cylinder like

so:


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EXAMPLE: Round to the nearest TENTH.

Top or bottom circle

A = r

A = (3.1)

A = (9.61)

A = 30.2

Rectangle

C = length

C = d

C = (6.2)

C = 19.5

Now the area

A = lw

A = 19.5(12)

A = 234

Now add:

30.2 + 30.2 + 234 =

SA = 294.4 in


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There is also a formula to find surface area of a cylinder.

Some people find this way easier:

SA = 2rh + 2r

SA = 2(3.1)(12) + 2(3.1)

SA = 2 (37.2) + 2(9.61)

SA = (74.4) + (19.2)

SA = 233.7 + 60.4

SA = 294.1 in

The answers are REALLY close, but not exactly the same.

Thats because we rounded in the problem.


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Find the radius and height of the cylinder.

Then Plug and Chug

Just plug in the numbers then do the math.

Remember the order of operations and youre

ready to go.

The formula tells you what to do!!!!

2rh + 2r means multiply 2()(r)(h) + 2()(r)(r)


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Volume of Prisms or Cylinders

You already know how to find the volume of a

rectangular prism: V = lwh

The new formulas you need are:

Triangular Prism V = ( bh)(H)

h = the height of the triangle and

H = the height of the cylinder

Cylinder V = (r)(H)


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Volume of a Triangular Prism

We used this drawing for our surface

area example. Now we will find the

volume.

V = ( bh)(H)

V = (6)(6)(9)

V = 162 mm

This is a

right

triangle, so

the sides are

also the base

and height.

Height of

the prism


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Try one:

Can you see thetriangular bases?

V = ( bh)(H)

V = ()(12)(8)(18)

V = 864 cm

Notice the prism is on

its side. 18 cm is the

HEIGHT of the prism.

Picture if you turned itupward and you can

see why its called

height.


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V = (r)(H)

V = ()(3.1)(12)

V = ()(3.1)(3.1)(12)

V = 396.3 in

Volume of a Cylinder

We used this drawing for oursurface area example. Now we will

find the volume.

optionalstep!


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Try one:

10 m

d = 8 m

V = (r)(H)

V = ()(4)(10)

V = ()(16)(10)

V = 502.7 mSince d = 8,

then r = 4

r = 4 = 4(4) = 16


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Here are the formulas you will need to know:

A = lw SA = 2rh + 2r

A = bh V = ( bh)(H)

A = r V = (r)(H)

C = d

and how to find the surface area of a prismby adding up the areas of all the surfaces

artysurface area & volume

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