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Chapter 19: Problem 29

The Sun has increased in radius by \(6 \%\) over the past \(4.56\) billion years. Its present-day radius is \(696,000 \mathrm{~km}\). What was its radius \(4.56\) billion years ago? (Hint: The answer is not \(654,000 \mathrm{~km}\).)

Short Answer

Expert verified
The radius of the Sun 4.56 billion years ago was about 657,547 km.

Step by step solution

01

Interpretation of the Problem

The Sun's current radius is 696,000 km and this represents an increase of 6% from the radius 4.56 billion years ago. So the task is to find out what the Sun's radius was 4.56 billion years ago. It should be noted that this increased size (696,000 km) is 106% of the original size (because 100% is the original size plus the 6% increase).
02

Setup of the Equation

Let \(x_\) be the original radius. Therefore, according to the problem, \(696,000 \mathrm{~km} = 106\% \) of \(x \). So, \(696,000 \mathrm{~km} = 1.06x\).
03

Solving the Equation

To find \(x_\), divide both sides of the equation by 1.06. So, \(\frac{696,000 \mathrm{~km}}{1.06} = x\). This equation will yield the value of \(x_\), which is the sun's radius 4.56 billion years ago.

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