SURFACE AREA AND VOLUME FORMULAS

Perimeter and Area Surface Area and Volume







PERIMETER AND AREA


Circle
A = (pi)r2
C = 2(pi)r 		Triangle
A = ½ bh
Parallelogram
A = bh 		Trapezoid
A = ½ (b1 + b2 )h
Rectangle
A = lw
P = 2l + 2w 		Square
A = s2
P = 4s












SURFACE AREA AND VOLUME FORMULAS

Prisms are solids that have a pair of congruent, parallel bases.
When we flatten out a net, we see that it consists of two bases with equal area and the lateral area.
The lateral area is the product of the perimeter of the base and the height of the solid.
Thus, the formula for the surface area of a prism is SA = 2B + LA , where the LA = ph (the perimeter times the height).
The volume is the product of the Base, B, and the height,h.
Thus, the formula for the volume of a prism is V = Bh.
Cylinders are a lot like prisms in that they have congruent, parallel bases.
We use the same formulas to find the surface area and volume of prisms.


SA = 2B + LA
SA = 2B + ph
SA = 2lw + 2(l+w)h		 SA = 2B + LA
SA = 2(pi)r2 + 2(pi)rh
V = Bh
V = lwh		 V = Bh
V = (pi)r2h
SA = 2B + LA
SA = 2(½bh)h + ph
SA = bhh + ph 		SA = 2B + LA
SA = 2(½(b1 + b2)h +ph
SA =(b1 + b2)h +ph
V = Bh
V = ½bhh 		V = Bh
V = (½(b1 + b2)h)h
SA = 2B + ph
SA = 2(s2) + (4s)(s)
SA = 6s2
V = Bh
V = (s2)s
V = s3
An italicized "h" refers to the height of the base. An unitalicized "h" refers to the height of the prism.



SURFACE AREA AND VOLUME OF PYRAMIDS AND CONES

The formulas for the surface area and volume of pyramids and cones are similar to those of prisms and cylinders.
One major difference is that pyramids and cones only have one base.
In addition, the sides of a cone are triangles, rather than rectangles. So, the lateral area is adjusted also.
One thing to consider is that pyramids have different heights
The slant height l, refers to the length from the base to the tip along one side of the pyramid.
It is used to find the lateral area.
The height, h, refers to the perpendicular distance from the base to the top-most part of the pyramid.
It is used to find the volume.
Thus the formula for the surface area of a pyramid or cone is SA = B + ½pl.
There is an interesting relationship between the volume of a prism and of a pyramid.
If you fill a pyramid with base, B, and height, h, and pour the contents into a prism with the same dimensions, you will be able to fill the prism three times.
Thus, the formula for the volume of a pyramid is V = 1/3Bh.
SA = B + LA
SA = B + ½pl 		SA = B + LA
SA = (pi)r2 + ½(2(pi)r)l
SA = (pi)r2 + (pi)rl
V = 1/3(Bh)
 V = 1/3((pi)r2h)








SA = 4(pi)r2 V = 4/3(pi)r3



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