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

The volume of the hemisphere is half the volume of a sphere. Thus:

$V = \frac{1}{2} \left( \frac{4}{3} \pi r^3 \right)$ Substituting (r = 4.2 \text{ cm}):

$V = \frac{1}{2} \left( \frac{4}{3} \pi (4.2)^3 \right)$

Calculating ((4.2)^3):

$(4.2)^3 = 74.088\text{ cm}^3$

Now substituting back:

$V = \frac{1}{2} \left( \frac{4}{3} \pi (74.088) \right)$

Calculating the value:

$V = \frac{4 \times 74.088 \times \pi}{6}$ $V \approx \frac{296.352 \times 3.14}{6} \approx 155.2 \text{ cm}^3$

The volume of the hemisphere is approximately 155 cm³, when rounded to 3 significant figures.