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Q 0.

Found in: Page 298


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Problem Zero: Read the section and make your summary of material

the rate can be calculated in terms of the factors that change with time.

See the step by step solution

Step by Step Solution

Step 1: Given information


A study of the formula for the surface and area of the right-circumference cylinder, cone, sphere, and rectangular box.

Step 2: Explanation

1. A rectangular box

V=x y zS=2 x y+2 y z+2 x z

2. Sphere


3. right circular cylinder


4. right circular cone


Step 3: Further calculation

There are two right triangle theorems.

The Pythagorean principle:a2+b2=c2

2. The law of similar triangles: hb=IIB,db=DB,dh=DII

The first derivative of a function f can be used to calculate the rate of change of a function f when it is increasing or decreasing.

Example: Both the radius and the height can be used to calculate the rate of change in volume of a right circular cylinder. Since the formula V=13πr2h determines the volume. Wherever the radius and height change, the volume V changes as well.

localid="1663925684234" V(t)=13πr(t)2h(t)dV(t)dt=13πr(t)2dh(t)dt+h(t)dr(t)2dtdV(t)dt=13πr(t)2dh(t)dt+h(t)r(t)dr(t)dt

Thus, the rate can be measured in terms of the variables associated over time.

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