Answer:
a) 3.41%
b) 24,795.62 km
c) 6,378.16 km
Step-by-step explanation:
a) To find what percent of Jupiter's radius that Mercury's radius is, we can divide Mercury's radius by Jupiter's radius:
[tex]\dfrac{r}{29.3r}[/tex]
↓ canceling the r's in the numerator and denominator
[tex]\dfrac{1}{29.3}[/tex]
↓ evaluating using a calculator
[tex]\approx 0.0341[/tex]
↓ converting to a percent
[tex]\boxed{3.41\%}[/tex]
b) We can solve for Neptune's radius (N) by setting Mars' radius equal to 13.7% of it:
[tex]\text{radius of Mars} = 13.7\% \cdot \text{radius of Neptune}[/tex]
↓ plugging in the known values
[tex]r + 957 = 13.7\% \cdot N[/tex]
↓ converting the percent to a decimal
[tex]r+957=0.137N[/tex]
↓ plugging in the radius of Mercury ([tex]r = 2440\text{ km}[/tex])
[tex]2440 + 957 = 0.137N[/tex]
↓ executing the addition on the left side
[tex]3397 = 0.137N[/tex]
↓ multiplying both sides by [tex]\frac{1}{0.137}[/tex]
[tex]\dfrac{1}{0.137} \cdot 3397 = \dfrac{1}{0.137} \cdot 0.137N[/tex]
↓ evaluating using a calculator
[tex]\boxed{N\approx 24795.62\text{ km}}[/tex]
c) We can solve for Earth's radius (E) by multiplying Mercury's radius by 261.4%:
[tex]E = r \cdot 261.4\%[/tex]
↓ converting the percent to a decimal
[tex]E = r \cdot 2.614[/tex]
↓ plugging in the radius of Mercury ([tex]r = 2440\text{ km}[/tex])
[tex]E = 2440 \cdot 2.614[/tex]
↓ evaluating using a calculator
[tex]\boxed{E\approx 6378.16\text{ km}}[/tex]
