surface area and volume
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Surface Area and VolumeTRANSCRIPT
7/17/2019 Surface Area and Volume
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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 =