Let's determine the volume of the asteroid 243 Ida, assuming it is a perfect sphere.
### Step-by-Step Solution:
1. Given Data:
- Mass of the asteroid = [tex]\( 4.0 \times 10^{16} \)[/tex] kilograms
- Radius of the asteroid = 16 kilometers
2. Convert the Radius to Meters:
Since most formulas in physics use meters, it is important to convert the radius from kilometers to meters.
[tex]\[
1 \text{ kilometer} = 1000 \text{ meters}
\][/tex]
Therefore,
[tex]\[
16 \text{ kilometers} = 16 \times 1000 \text{ meters} = 16000 \text{ meters}
\][/tex]
3. Calculate the Volume of the Asteroid:
We will use the formula for the volume of a sphere:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
4. Substitute the Radius into the Formula:
[tex]\[
V = \frac{4}{3} \pi (16000)^3
\][/tex]
5. Calculate the Volume:
After performing the calculation, we find:
[tex]\[
V \approx 1.7157284678805 \times 10^{13} \text{ cubic meters}
\][/tex]
6. Summary of Results:
- The mass of the asteroid is [tex]\( 4.0 \times 10^{16} \)[/tex] kilograms.
- The volume of the asteroid, assuming it is spherical, is approximately [tex]\( 1.7157284678805 \times 10^{13} \)[/tex] cubic meters.
Thus, we have determined the mass and calculated the volume of the asteroid 243 Ida, assuming it to be a perfect sphere.
