Derivation of Formula for Total Surface Area of the Sphere by Integration

Instructions:

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question 1 of 3

An arc subtends an angle of π radians along a circle with a radius of 4 inches. The arclength is _____.

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1. The formula relating the differential arclength, ds, the radius, R'', and the differential angle, dθ, is _____.

2. Given the equation r = R cos θ, the value of r at θ = 90o is _____.

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About This Quiz and Worksheet

With this combination of a quiz and worksheet you can see what you know about finding a sphere's area with integration. Questions ask about the arclength of a given measurement as well as the total surface area of a circle whose radius is doubled.

Quiz and Worksheet Goals

Expect to see the topics mentioned below in the questions of the quiz:

  • The formula for differential arclength, radius, and differential angle
  • Finding the value of a sphere's radius at a given angle
  • Finding the differential area
  • Doubling the radius of a given circle

Skills Practiced

  • Information recall - remember what you have learned about cosines and the value of 'r'
  • Defining key concepts - ensure that you know the steps of a formula for differential arclength, radius, and differential angle
  • Knowledge application - use what you know to answer questions about doubling the radius of a circle

Additional Learning

For more help, head to the lesson titled Derivation of Formula for Total Surface Area of the Sphere by Integration. With it, you can access the following other topics:

  • The formula for total surface area
  • The r-R relationship
  • Anti-derivatives
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