Assuming that the Earth is a sphere of radius 6378 km: (i) Find the length of the equator, correct to the nearest km - Leaving Cert Mathematics - Question b - 2015

To find the volume of a sphere, the formula is:

$V = \frac{4}{3} \pi r^{3}$

Substituting the radius:

$V = \frac{4}{3} \pi (6378)^{3} \approx 1.0867 \times 10^{12} \text{ km}^3$

Thus, the volume of the Earth can be expressed as:

$V \approx 1.087 \times 10^{12} \text{ km}^3$

Rounding to three decimal places, we find:

$a = 1.087$

To find how many times greater the mass of the Sun is than the mass of the Earth, we use the following equation:

$\text{Number of times} = \frac{\text{Mass of Sun}}{\text{Mass of Earth}}$

Substituting the masses:

$\text{Number of times} = \frac{1.99 \times 10^{30}}{5.97 \times 10^{24}} \approx 333.333$

Rounding to the nearest whole number, we find it is approximately 333.