Is the following statement about our solar system true or false?
The volume of Earth is more than ten times the volume of Mercury. A. True B. False
The Correct Answer and Explanation is :
The correct answer is A. True.
To understand why this statement is true, we need to compare the volumes of Earth and Mercury. The volume of an object can be calculated using the formula for the volume of a sphere, given by ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere.
- Volume of Mercury: Mercury has a radius of approximately 2,439.7 kilometers. Using the formula:
[
V_{Mercury} = \frac{4}{3} \pi (2,439.7)^3 \approx 6.083 \times 10^{10} \text{ km}^3
] - Volume of Earth: Earth has a radius of about 6,371 kilometers. Using the same formula:
[
V_{Earth} = \frac{4}{3} \pi (6,371)^3 \approx 1.08321 \times 10^{12} \text{ km}^3
] - Comparison: Now, we compare the two volumes:
- Volume of Mercury: ( 6.083 \times 10^{10} \text{ km}^3 )
- Volume of Earth: ( 1.08321 \times 10^{12} \text{ km}^3 )
To determine how many times larger Earth’s volume is compared to Mercury’s, we can divide the volume of Earth by the volume of Mercury:
[
\frac{V_{Earth}}{V_{Mercury}} \approx \frac{1.08321 \times 10^{12}}{6.083 \times 10^{10}} \approx 17.8
]
This calculation shows that Earth’s volume is approximately 17.8 times greater than that of Mercury. Therefore, the statement “the volume of Earth is more than ten times the volume of Mercury” is true.
In summary, Earth’s significantly larger volume compared to Mercury can be attributed to its larger size and mass, which is characteristic of the terrestrial planets in our solar system.