Chapter 34, Problem 1TS

If you were to travel straight up from the core of our galaxy and then look back, you would have a grand view of the Milky Way’s spiral shape. If the distance from the core to the outer edges was $50,000\text{ light-years}$, how much surface area are you looking at? Assume the galaxy to be a circle whose area can be found by the equation $\text{area}=\pi r^2$.

To determine

The surface area of the galaxy.

Answer to Problem 1TS

The surface area of the galaxy is $7.85\times {10}^9{\text{light-years}}^2$.

Explanation of Solution

Given info: The distance from the core of the galaxy to the outer edges is $50000\text{light-years}$.

Write the expression for area.

$A=\pi r^2$

Here,

$A$ is the area

$r$ is the radius

Substitute $50000\text{light-years}$ for $r$ in above expression to get $A$.

$\begin{array}{c}A=\pi \times {\left(50000\text{light-years}\right)}^2\\ =\frac{22}{7}\times 2500000000{\text{light-years}}^2\\ =7.85\times 1^9{\text{light-years}}^2\end{array}$

Conclusion:

Therefore, the surface area of the galaxy is $7.85\times {10}^9{\text{light-years}}^2$.