Precalc0011to0016-page34

Precalc0011to0016-page34 - meters , say, then surface areas...

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(Section 0.15: Plane and Solid Geometry) 0.15.2 PART C: SOLID GEOMETRY Description Solid Formulas Rectangular Box with dimensions l , w , and h Volume = lwh Surface Area = 2 lw + 2 wh + 2 lh (See Note 1.) Right Circular Cylinder with base radius r and height h Volume = ± r 2 h Lateral Surface Area = 2 rh Total Surface Area = 2 rh + 2 r 2 (See Note 2.) Right Circular Cone with base radius r and height h Volume = 1 3 r 2 h Lateral Surface Area = rl , with slant height l = r 2 + h 2 Total Surface Area = rl + r 2 (See Note 3.) Sphere with radius r Volume = 4 3 r 3 Surface Area = 4 r 2 In calculus , you may verify some of these formulas. • We can use dimensional analysis to help check our formulas. If lengths are measured in
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Unformatted text preview: meters , say, then surface areas are measured in square meters , and volumes are measured in cubic meters . For example, if the radius r of a sphere is measured in meters , then the volume formula V = 4 3 r 3 does, in fact, yield a volume in cubic meters . This analysis prevents us from accidentally switching this formula with the formula for surface area. Note 1 (Box) The volume equals the rectangular base area times the height . The surface area is the sum of the areas of the six sides. Think of the walls, floor, and ceiling of a room....
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This document was uploaded on 12/29/2011.

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