The Sun’s radius is approximately 7E8 meters. What is its volume?
The correct answer and explanation is :
The Sun’s radius is approximately 7×1087 \times 10^8 meters. To find its volume, we treat the Sun as a sphere and use the formula for the volume of a sphere: V=43πr3V = \frac{4}{3} \pi r^3
Step 1: Write down the radius
r=7×108 metersr = 7 \times 10^8 \text{ meters}
Step 2: Cube the radius
r3=(7×108)3=73×(108)3=343×1024=3.43×1026r^3 = (7 \times 10^8)^3 = 7^3 \times (10^8)^3 = 343 \times 10^{24} = 3.43 \times 10^{26}
Step 3: Calculate the volume
V=43π×3.43×1026≈4.18879×3.43×1026V = \frac{4}{3} \pi \times 3.43 \times 10^{26} \approx 4.18879 \times 3.43 \times 10^{26}
Using π≈3.14159\pi \approx 3.14159, V≈4.18879×3.43×1026≈14.37×1026=1.437×1027 cubic metersV \approx 4.18879 \times 3.43 \times 10^{26} \approx 14.37 \times 10^{26} = 1.437 \times 10^{27} \text{ cubic meters}
Final answer:
1.44×1027 m3\boxed{1.44 \times 10^{27} \text{ m}^3}
Explanation:
The Sun is often approximated as a perfect sphere for many astrophysical calculations because, despite its gaseous nature and complex internal dynamics, its shape is very close to spherical due to gravity pulling matter equally from all directions.
To find the volume of a sphere, we use the formula V=43πr3V = \frac{4}{3} \pi r^3, which comes from integral calculus and geometric principles. The radius rr is raised to the third power because volume is a three-dimensional measurement.
In this case, the Sun’s radius is about 7×1087 \times 10^8 meters, which is 700 million meters or roughly 700,000 kilometers — about 109 times the radius of Earth. Cubing this large radius results in an enormous number, approximately 3.43×10263.43 \times 10^{26}.
Multiplying by 43π\frac{4}{3} \pi, which is roughly 4.19, gives the volume as roughly 1.44×10271.44 \times 10^{27} cubic meters. This value highlights the sheer scale of the Sun compared to planets; for example, Earth’s volume is about 1.08×10211.08 \times 10^{21} cubic meters, making the Sun’s volume over a million times greater.
Understanding the Sun’s volume is fundamental in astrophysics for calculating its density (mass divided by volume), which in turn helps scientists understand its structure, nuclear fusion processes, and life cycle. The vast volume also correlates with the enormous amount of energy produced by the Sun, sustaining life on Earth and driving the solar system’s dynamics.