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

Instructions:

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

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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