The volume, V, of a sphere is given by the formula $$V = \frac{4}{3} \pi r^3,$$ where r is the radius of the sphere - HSC - SSCE Mathematics Standard - Question 16 - 2021 - Paper 1

To calculate the volume of the bottom half of the sphere, we need to use the formula for the volume of a sphere and then take half of that volume.

1. Calculate the volume of a full sphere with radius 2 metres:

   $V = \frac{4}{3} \pi (2)^3$

   First, find ((2)^3 = 8). Thus,

   $V = \frac{4}{3} \pi \times 8 = \frac{32}{3} \pi$

2. Now, take half of that volume to get the volume of the tank:

   $V_{tank} = \frac{1}{2} \times \frac{32}{3} \pi = \frac{16}{3} \pi$

3. Using the value of (\pi \approx 3.14):

   $V_{tank} \approx \frac{16}{3} \times 3.14 \approx 16.7553\ m^3$

4. Rounding to one decimal place gives:

   $V_{tank} \approx 16.8\ m^3$