Question

# If the sun expanded to a radius 100 times its present radius, what would its density be? (Hint: The volume of a sphere is $\frac{4}{3} \pi R^3.)$

Solution

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$\text{\textcolor{#4257b2}{The density formula is }}$

$\boxed{Density (\rho) = mass(m) / volume(V)}$

$\text{\textcolor{#c34632}{The mass of the Sun is }}$ $M_{\odot}=1.99 \times 10^{30}$ kg $=1.99 \times 10^{33}$ grams

$\text{\textcolor{#c34632}{The radius of the Sun is}}$ $R_{\odot}=6.96 \times 10^5$ km $=6.96 \times 10^{10}$ cm,

$V =\frac{4}{3} \pi R_{\odot}^3 = (\frac{4}{3})(\pi)(6.96 X 10^{10}\hspace{2mm}cm)^3$

$\text{\color{white}.}$      $= 1.41 \times 10^{33}\hspace{2mm} cm^3$

$\rho = M / V = (1.99 \times 10^{33} \hspace{2mm} gm) / (1.41 \times 10^{33} \hspace{2mm} cm^3$

$= 1.41\hspace{2mm} gm/cm^3$

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