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7.1 Surface Area and Volume
1. Learn and use the formulas to find Surface Area and Volume of a rectangular prism and cube. 2. Learn Surface Area to Volume ratios.
 * Objectives:**

For a rectangular prism: //S is surface area, l is length, w is width, and h is height// S = 2lw + 2lh + 2wh
 * Surface Area and Volume Formulas**

//V is volume and l, w, and h remain the same// V = lwh

For a cube: //S is surface area, s is side// S = 6s^2

//V is volume, s remains the same.// V = s^3

Basically, the S:V ratio is just Surface Area (S) over (/) volume it looks like this; S/V or S:V
 * Ratios S:V**

If the length of a rectangular prism is 4, the height is 6, and the width is 2. Using the formulas above, find the surface area and volume. And remember if you replace a value always put it in parentheses.
 * Example**

S = 2(4)(2) + 2(4)(6) + 2(2)(6)

S = 16 + 48 + 24

S = 88

V = lwh

V = (4)(2)(6)

V = 48

Now, take the S and V and make a fraction out of it, S as your numerator (top number) and V as your denominator (bottom number). You just made a S:V ratio! Good job!

You get a cookie!

**7.2 Surface Area and Volume of Prisms**
1. Learn and use the formulas for the Surface Area and Volume of right prisms. 2. Learn Cavalieri's Principle.
 * Objectives**

//Altitude-// A segment with endpoints that are in, and is perpendicular to, both bases, or planes containing the bases, of the rectangular prism.
 * Vocabulary**

//Height-// The measured length of an altitude.

//Surface Area-// S, //Lateral Area-// //L,// //Base Area-// //B, Perimeter//- //p, and Height//- //h//
 * Surface Area and Volume Formulas**

SL + 2B **//__OR__//** Shp + 2B

By the way, Lateral area is found by

//Volume- V, B and h stay the same//

V = Bh

If two solids have the same height, and the cross sections formed by several parallel planes (of the bases) are the same. Then both solids have equal areas, therefore, the same volume.
 * Cavalieri's Principle**


 * 10 Sample Problems

1**. Volume of a Triangular prism. If B= 10 and h= 6 V=Bh V=(10)(6) V=60 units^3

S=hp+2B =(4)(9)+2(8) =36+16 = 52 units^2
 * 2.** Surface Area of a Triangular prism. If h=4 p=9 and B=8

V=(1/3)Bh V=(1/3)(14)(7) V=32.6667
 * 3.** Volume of a Pyramid. If B=14 and h=7

S=(1/2)lp+B S=(1/2)(6)(3)+(15) S=24
 * 4.** Surface Area of a Pyramid. If l=6 p=3 and B=15

S=(3.14)(6)^2(5) S=565.48
 * 5.** Volume of a cylinder. If r=6 and h=5

S=2(3.14)(8)(3)+2(3.14)(8)^2 S=552.92
 * 6.** Surface area of a cylinder. If r=8 and h=3

V=(1/3)(3.14)(6)^2(10) V=376.99
 * 7.** Volume of a cone. If r=6 and h=10

S=(3.14)(17)(9)+(3.14)(17)^2 S=1288.58
 * 8.** Surface area of a cone. If r=17 and l=9

V=(4/3)(3.14)(28)^3 V=91952.32
 * 9.** Volume of a Sphere. If r=28

S=4(3.14)(45)^2 S=25446.90
 * 10.** Surface area of a sphere. If r=45