7 A sphere has a radius of \( 6.4 \times 10^{6} \) metres. Calculate the volume of this sphere. Give your answer in standard form to 1 decimal place.

To calculate the volume \( V \) of a sphere, you can use the formula: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius. Given the radius \( r = 6.4 \times 10^6 \) metres, we can substitute this into the formula: \[ V = \frac{4}{3} \pi (6.4 \times 10^6)^3 \] Calculating \( (6.4 \times 10^6)^3 \): \[ (6.4)^3 = 262.144 \] \[ (10^6)^3 = 10^{18} \] Thus, \[ (6.4 \times 10^6)^3 = 262.144 \times 10^{18} \] Now substituting back into the volume formula: \[ V = \frac{4}{3} \pi (262.144 \times 10^{18}) \approx \frac{4}{3} \times 3.14159 \times 262.144 \times 10^{18} \] Calculating \( \frac{4}{3} \times 3.14159 \approx 4.18879 \): \[ V \approx 4.18879 \times 262.144 \times 10^{18} \] \[ \approx 1094.396 \times 10^{18} \] Now putting it into standard form: \[ V \approx 1.094396 \times 10^{21} \] Rounding to 1 decimal place gives: \[ V \approx 1.1 \times 10^{21} \text{ cubic metres} \] So, the volume of the sphere is: \[ \boxed{1.1 \times 10^{21}} \text{ cubic metres} \]