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

Question

Asked on April 20, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-20T22:08:15.850Z

Hey Water — ready when you are. Here are the solutions for Item 6: Task (a): Determine the quantity of porridge, in litres, that will be served to each of the 500 students if the caterer gets the larger container and each student is to receive the same quantity. Step 1: Find the ratio of the surface areas. Let SA_1 be the surface area of the original container and SA_2 be the surface area of the larger container. (SA_2)/(SA_1) = 150,000 cm^296,000 cm^2 = (150)/(96) = (25)/(16) Step 2: Determine the linear scale factor (k). Since the ratio of surface areas is k^2, we have: k^2 = (25)/(16) k = sqrt((25)/(16)) = (5)/(4) Step 3: Determine the ratio of the volumes. Since the ratio of volumes is k^3, we have: (V_2)/(V_1) = k^3 = ((5)/(4))^3 = (5^3)/(4^3) = (125)/(64) Step 4: Calculate the volume of the larger container (V_2). The volume of the original container (V_1) is 128,000 cm^3. V_2 = V_1 × (125)/(64) = 128,000 cm^3 × (125)/(64) V_2 = 2,000 × 125 cm^3 = 250,000 cm^3 Step 5: Convert the volume to litres. Since 1 litre = 1,000 cm^3: V_2 = (250,000)/(1,000) litres = 250 litres Step 6: Calculate the quantity of porridge per student. There are 500 students. Quantity per student = Total volumeNumber of students = 250 litres500 = 0.5 litres The quantity of porridge served to each student will be 0.5 litres. Task (b): Compute the net income for the cook. Step 1: Calculate the total allowances. Gross monthly income = Shs 853,500 Transport allowance = Shs 115,500 Housing allowance = Shs 81,150 Lunch allowance = 10\% of gross monthly income Lunch allowance = 0.10 × 853,500 = Shs 85,350 Utilities allowance = Shs 35,500 Total allowances = Transport + Housing + Lunch + Utilities Total allowances = 115,500 + 81,150 + 85,350 + 35,500 = Shs 317,500 Step 2: Calculate the taxable income. Taxable income = Gross monthly income - Total allowances Taxable income = 853,500 - 317,500 = Shs 536,000 Step 3: Calculate the income tax using Table 3. 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 = Shs 145,000 Tax = $0.13 × 145

Accepted Answer · 2026-04-20T22:08:15.850Z

Hey Water — ready when you are. Here are the solutions for Item 6: Task (a): Determine the quantity of porridge, in litres, that will be served to each of the 500 students if the caterer gets the larger container and each student is to receive the same quantity. Step 1: Find the ratio of the surface areas. Let SA_1 be the surface area of the original container and SA_2 be the surface area of the larger container. (SA_2)/(SA_1) = 150,000 cm^296,000 cm^2 = (150)/(96) = (25)/(16) Step 2: Determine the linear scale factor (k). Since the ratio of surface areas is k^2, we have: k^2 = (25)/(16) k = sqrt((25)/(16)) = (5)/(4) Step 3: Determine the ratio of the volumes. Since the ratio of volumes is k^3, we have: (V_2)/(V_1) = k^3 = ((5)/(4))^3 = (5^3)/(4^3) = (125)/(64) Step 4: Calculate the volume of the larger container (V_2). The volume of the original container (V_1) is 128,000 cm^3. V_2 = V_1 × (125)/(64) = 128,000 cm^3 × (125)/(64) V_2 = 2,000 × 125 cm^3 = 250,000 cm^3 Step 5: Convert the volume to litres. Since 1 litre = 1,000 cm^3: V_2 = (250,000)/(1,000) litres = 250 litres Step 6: Calculate the quantity of porridge per student. There are 500 students. Quantity per student = Total volumeNumber of students = 250 litres500 = 0.5 litres The quantity of porridge served to each student will be 0.5 litres. Task (b): Compute the net income for the cook. Step 1: Calculate the total allowances. Gross monthly income = Shs 853,500 Transport allowance = Shs 115,500 Housing allowance = Shs 81,150 Lunch allowance = 10\% of gross monthly income Lunch allowance = 0.10 × 853,500 = Shs 85,350 Utilities allowance = Shs 35,500 Total allowances = Transport + Housing + Lunch + Utilities Total allowances = 115,500 + 81,150 + 85,350 + 35,500 = Shs 317,500 Step 2: Calculate the taxable income. Taxable income = Gross monthly income - Total allowances Taxable income = 853,500 - 317,500 = Shs 536,000 Step 3: Calculate the income tax using Table 3. 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 = Shs 145,000 Tax = $0.13 × 145

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

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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

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