# 7.1 SURFACE AREA AND VOLUME

The surface area and vol ume of an objec rectangular prizmt is the total area of all the exposed surfaces of the object.The volume of a solid object is the number of nonoverlapping unit cubes that will exactly fill the interior of the figure.

SURFACE AREA AND VOLUME FORMULAS

the surafce area,s,and volume v of a right cube[[http://education.yahoo.com/homework_help/math_help/solutionimages/miniprealggt/9/1/1/miniprealggt_9_1_1_17_80/f-636-11-pr-q.gif|]]
S=2L+2WH+2LH and V=LWH

The surface area,S,and volume,V,of a cube with side s are
S=6s2 and V,of a cube with side s.
7.2 surface area and volume of prizms7.2 surface area and volume of prizmsthe 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 feetthe 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

## 7.5 surface area and volume of cones

 The volume of a cone is: π × r2 × (h/3)
cone facts
has a flat base
it has one curved side
because it has a curved side is not a polyhedron