quiz #2 begin date: 10/20/2025 12:01:00 am due date: 10/26/2025 11:59:00
problem 16: (5% of assignment value)
the planet saturn has a mass of 5.7×10²⁶ kg and a radius of 58,000 km.
part (a)
calculate the volume v of saturn in m³.
v =
m³
part (b)
calculate the density ρ of saturn in kg/m³.
part (c)
water has a density of approximately 1×10³ kg/m³. is saturn more or less dense than w

Question

Accepted Answer

# Explanation:
## Step1: Convert radius from km to m
Given radius $r = 58000\space km=58000\times10^{3}\space m = 5.8\times 10^{7}\space m$
## Step2: Use the formula for the volume of a sphere $V=\frac{4}{3}\pi r^{3}$
Substitute $r = 5.8\times 10^{7}\space m$ into the formula:
$$
\begin{align*}
V&=\frac{4}{3}\times\pi\times(5.8\times 10^{7})^{3}\
&=\frac{4}{3}\times\pi\times5.8^{3}\times10^{21}\
&=\frac{4}{3}\times\pi\times195.112\times10^{21}\
&\approx\frac{4}{3}\times3.14\times195.112\times 10^{21}\
&=\frac{2451.77984}{3}\times10^{21}\
&\approx8.17\times 10^{23}\space m^{3}
\end{align*}
$$

# Answer:
$8.17\times 10^{23}$

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QUESTION IMAGE

Question

Explanation:

Step1: Convert radius from km to m

Step2: Use the formula for the volume of a sphere \(V=\frac{4}{3}\pi r^{3}\)

Answer: