Here is a frustum of a cone - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

The volume of a hemisphere is given by the formula:

$V_{hemisphere} = \frac{2}{3} \pi r^3$

For the hemisphere with a diameter of 7.2 cm, the radius is:

$r = \frac{7.2}{2} = 3.6 \text{ cm}$

Therefore, the volume of the hemisphere is:

$V_{hemisphere} = \frac{2}{3} \pi (3.6)^3 = \frac{2}{3} \pi (46.656) \approx 97.34 \text{ cm}^3$

The total volume of solid S is the sum of the volumes of the frustum and the hemisphere:

$V_{S} = V_{frustum} + V_{hemisphere} = 44.54 + 97.34 \approx 141.88 \text{ cm}^3$

Next, we calculate the mass of the frustum and the hemisphere. The densities provided are as follows:

• Density of the frustum = 2.4 g/cm³
• Density of the hemisphere = 4.8 g/cm³

So, the mass of the frustum is:

$m_{frustum} = V_{frustum} \times 2.4 \approx 44.54 \times 2.4 \approx 106.89 \text{ g}$

And for the hemisphere:

$m_{hemisphere} = V_{hemisphere} \times 4.8 \approx 97.34 \times 4.8 \approx 466.35 \text{ g}$

The total mass of solid S is:

$m_{S} = m_{frustum} + m_{hemisphere} = 106.89 + 466.35 \approx 573.24 \text{ g}$

Finally, the average density of solid S can be calculated using the formula:

$\text{Density} = \frac{\text{Total mass}}{\text{Total volume}}$

Substituting the calculated values gives:

$\text{Density} = \frac{573.24}{141.88} \approx 4.04 \text{ g/cm}^3$