The diagram shows a solid shape - Edexcel - GCSE Maths - Question 16 - 2019 - Paper 1

The formula for the volume of a hemisphere is: $V_{hemisphere} = \frac{2}{3} \pi r^3$ The radius (r) of the hemisphere is also:

$r = \frac{6}{2} = 3 \text{ cm}$

Now substituting the radius into the hemisphere volume formula: $V_{hemisphere} = \frac{2}{3} \pi (3^3) = \frac{2}{3} \pi (27) = 18\pi \text{ cm}^3$

The total volume of the shape is the sum of the volumes of the cone and hemisphere: $V_{total} = V_{cone} + V_{hemisphere}$

Substituting the previously found volumes: $V_{total} = 30\pi + 18\pi = 48\pi \text{ cm}^3$

Since the total volume is given as $k \text{ cm}^3$ and we found that: $V_{total} = 48\pi$

Thus, equating: $48\pi = k \text{ cm}^3$

Dividing through by $\pi$ gives: $k = 48$.