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Chapter 11: Problem 15

Solve each formula for the indicated letter. Assume that all variables represent nonnegative numbers. \(A=4 \pi r^{2},\) for \(r\) (Surface area of a sphere of radius \(r\) )

Short Answer

Expert verified
r = \sqrt{\frac{A}{4\pi}}.

Step by step solution

01

Understand the equation

The given equation is the formula for the surface area of a sphere: \[ A = 4 \pi r^2 \]. We need to solve this formula for the variable \( r \).
02

Isolate \(r^{2}\)

To isolate \(r^{2}\), divide both sides of the equation by \(4 \pi\): \[ \frac{A}{4 \pi} = r^2 \].
03

Solve for \(r\)

To solve for \(r\), take the square root of both sides: \[ r = \sqrt{\frac{A}{4\pi}} \].
04

Write the final formula

The final formula for \(r\) is: \[ r = \sqrt{\frac{A}{4\pi}} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

surface area of a sphere
The surface area of a sphere is a measure of the total area that the surface of the sphere occupies. It is given by the formula \( A = 4 \pi \ r^{2} \). This formula tells us how much space the surface of a sphere covers in square units.

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