A caterer has two cylindrical containers for serving porridge. The original container has a surface area of 96,000 cm² and a volume of 128,000 cm³. The larger container has a surface area of 150,000 c

Let $SA_1$ be the surface area of the original container and $SA_2$ be the surface area of the larger container.

$$\frac{SA_2}{SA_1} = \frac{150,000 \text{ cm}^2}{96,000 \text{ cm}^2} = \frac{150}{96} = \frac{25}{16}$$

Since the ratio of surface areas is $k^2$, we have:

$$k^2 = \frac{25}{16}$$ $$k = \sqrt{\frac{25}{16}} = \frac{5}{4}$$

Since the ratio of volumes is $k^3$, we have:

$$\frac{V_2}{V_1} = k^3 = \left(\frac{5}{4}\right)^3 = \frac{5^3}{4^3} = \frac{125}{64}$$

The volume of the original container ($V_1$) is $128,000 \text{ cm}^3$.

$$V_2 = V_1 \times \frac{125}{64} = 128,000 \text{ cm}^3 \times \frac{125}{64}$$ $$V_2 = 2,000 \times 125 \text{ cm}^3 = 250,000 \text{ cm}^3$$

Since $1 \text{ litre} = 1,000 \text{ cm}^3$:

$$V_2 = \frac{250,000}{1,000} \text{ litres} = 250 \text{ litres}$$

There are 500 students.

$$\text{Quantity per student} = \frac{\text{Total volume}}{\text{Number of students}} = \frac{250 \text{ litres}}{500} = 0.5 \text{ litres}$$

The quantity of porridge served to each student will be $\boxed{\text{0.5 litres}}$.

Task (b): Compute the net income for the cook.

Gross monthly income = Shs 853,500
Transport allowance = Shs 115,500
Housing allowance = Shs 81,150
Lunch allowance = $10\%$ of gross monthly income

$$\text{Lunch allowance} = 0.10 \times 853,500 = \text{Shs } 85,350$$

Utilities allowance = Shs 35,500

Total allowances = Transport + Housing + Lunch + Utilities

$$\text{Total allowances} = 115,500 + 81,150 + 85,350 + 35,500 = \text{Shs } 317,500$$

Taxable income = Gross monthly income - Total allowances

$$\text{Taxable income} = 853,500 - 317,500 = \text{Shs } 536,000$$

The taxable income is Shs 536,000.

• First band (Shs 0 - 105,000): Tax = Shs 0
• Second band (Shs 105,001 - 250,000): Amount = $250,000 - 105,000 = \text{Shs } 145,000$ Tax = $0.13 \times 145