Question

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 = 8.17 · 10²³
v = 8.170 × 10²³ m³ answer saved successfully!
part (b)
calculate the density ρ of saturn in kg/m³.
ρ = kg/m³
degrees radians
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hints:
part (c)

Explanation:

Step1: Recall the density formula

Density formula is \(
ho=\frac{m}{V}\), where \(m\) is mass and \(V\) is volume.

Step2: Substitute the given values

Given \(m = 5.7\times10^{26}\text{ kg}\) and \(V=8.17\times 10^{23}\text{ m}^3\).
Substitute into the formula: \(
ho=\frac{5.7\times 10^{26}}{8.17\times 10^{23}}\).

Step3: Calculate the value

Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\), we have \(\frac{5.7}{8.17}\times10^{26-23}\).
\(\frac{5.7}{8.17}\approx0.7\), and \(10^{26 - 23}=10^{3}\).
So \(
ho\approx0.7\times10^{3}\text{ kg/m}^3 = 700\text{ kg/m}^3\).

Answer:

\(700\text{ kg/m}^3\)