Surface+and+volume+of+prizms

=**7.2 surface area and volume of prizms**=

the surface area of a right prizm with lateral area L base area B perimeter area P and height h is:

S=L+2B or S=hp+2B

cavalieris principle

if two solid have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas ,then the two solids have equal volumes

volume of a prism

The volume of a prism with height h and base area B is V=Bh

__//REMEMBER THE SURFACE AREA OF A PRISM MAY BE BROKEN DOWN INTO TWO PARTS:THE AREA OF THE// BASES//,OR BASE AREA,AND THE AREA OF THE LATERAL FACES ,OR LATERAL ARE//__

=7.3 surface area and volume of piramids=



diferent types of pyramids

triangular pyramid square pyramid pentagonal pyramid

hexagonal pyramid and so......

the surface aret of a S of a regular pyramid with lateral area L,base area B,perimeter of the base P,and slant heifgt L is

S=L+B or S=1/2lp+B

example

the roof of a gazebo is a regular octagonal pyramid with a base edge of 4 feet and a slant heigh oh 6 feet.find the area of the roof.if roofing materials cost is $3.50 per square foot,find the cost of covering the roof with this material. solution the area of the roof is the lateral of yhe pyramid L=1/2 LP=(6)(8X4)=96 square feet 96 square feet x $3.50 per square foot=$336.00

the volume V, of a pyramid with height h and base B is

V=1/3bh EXAMPLE

the pyramid khufu is a regular square pyramid with a base edge aproximately 776 feet and an original height of 481 feet. the mistone used to construct the pyramid weighs apraximately 167 pounds per cubic food. estimate the weight of the pyramid of khufu. solution the volume of the pyramid is is found as follows; V=1/3BH =1/3(776)(481) = 96,548,885 cubic feet the weigh in pounds is 96,548,885 cubic feet X 167 pounds per cubic foot =16,123,663,850 pounds or 8,061,831 tons.

7.4 surface area and volume of cylinders


The surface area of a right cylider with latal area L,base area B radius r, and heigh his

S=L=2B or S=(2)3.1416h=(2)3.1416r2

example

a penny is a right cylinder with a diameter of 19.05 millimeters and a thicknes of 1.55 millimeters.ignoring the raised design,estimate the surface area of a penny solution

s=2perh+2 pe r cube

s=2 pe (9.525)(1.55)+2 pe(9.525)saquare=663.46 square miles

the volume V of a cylinder with radius r, height h, and base area B is

V=Bh or V=pe r square h

example

a tank has a lenght of 31 feet 6 1/2 inches and an outer diameter of 8 feet 0inches .assuminga wall thicknes of about 2 inches ,what is the volume of the tank?

V=pe r cube h=pe (3.833)(28.667)=1323 cubic feet