The diagram shows a hemisphere with diameter 8.4cm - Edexcel - GCSE Maths - Question 20 - 2019 - Paper 2

The volume of a sphere is given by the formula ( V = \frac{4}{3} \pi r^3 ). For a hemisphere, the volume is half of that:

[ V_{hemisphere} = \frac{1}{2} \times \frac{4}{3} \pi r^3 ]

Substituting the radius:

[ V_{hemisphere} = \frac{1}{2} \times \frac{4}{3} \pi (4.2)^3 ]

Let's calculate ( (4.2)^3 ):

[ (4.2)^3 = 74.088 ]

Now substituting back into the volume formula:

[ V_{hemisphere} = \frac{1}{2} \times \frac{4}{3} \pi \times 74.088 = \frac{4}{6} \pi \times 74.088 = \frac{2}{3} \pi \times 74.088 ]

Calculating this gives approximately:

[ V_{hemisphere} \approx \frac{2 \times 3.14159 \times 74.088}{3} \approx 155.22 \text{ cm}^3 ]

Rounding 155.22 to 3 significant figures, the final answer is:

[ V_{hemisphere} \approx 155 \text{ cm}^3 ]