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Surface AreaSurface Area

& Volume& Volume

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Defnition: The sum o the areas o all o the aces o a three-dimensional fgure.

Ex. How much construction paper will I need toft on the outside o the shape?

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Defnition: The measure in cubic units o the interior o asolid fgure or the space enclosed b! a solid

fgure.

Ex. How much sand will it hold?

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Ex:How much construction paper would I need to fton the outside o a particular rectangular prism?

"ormula:

#.$. % &'( ) &'h ) &(h

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Ex:How much sand would I need to fll the inside o aparticular rectangular prism?

"ormula:

* % '+(+h

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Cylinders

,!linder: $ right prism with circular bases.

 The base area is the area o the circle:

 The lateral area is the area of the rectangle:2πrh

h

2 rπ

h

2 rπ

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L.S.A = 2πrh

 T.S.A. = 

2πr( r + h )

  V = Cross sectional area * height

=

2r hπ  

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2r 

l

2r 

l

the area of the curved part of the cone. (Excluding the circular base)

 L.S.A = !" # perimeter of the base # slant height

 = $ # "%r # l

 = %r l

total surface area of a right cone is . S. A. = %rl ' %r".

Surface area

of cone

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( V ) = % r"h

r 

h h

r 

Volume of

a one

*ere the vertical height

and radius of c+linder &cone are same. 

( volume of cone) = volume of c+linder

 V = ! % r"h

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#urace $rea o a #phere The surace area o a sphere is our times the

product o pi and the suare o the radius othe sphere.

2. . 4S A r π  =

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*olume o a #phere The /olume o a sphere is our thirds the product o

pi and the cube o the radius o the sphere.

34

3V r π  =