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Simphiwe makes candles as shown in the pictures below - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1

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Simphiwe makes candles as shown in the pictures below. He uses a cylindrical mould to make the candles. He also carves horsesheads in some of the cylindrical candles... show full transcript

Worked Solution & Example Answer:Simphiwe makes candles as shown in the pictures below - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1

Step 1

Determine the minimum length and width of the box he needs if the candles are tightly packed, touching each other in the box.

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Answer

To find the dimensions of the box needed for 12 cylindrical candles, we start with the dimensions of each candle.

Given that the diameter of each candle is 10.4 cm, the radius (r) will be:
r=10.42=5.2 cmr = \frac{10.4}{2} = 5.2 \text{ cm}

The minimum width (W) of the box can be calculated as the total diameter of 4 candles aligned in one row: W=4×10.4=41.6 cmW = 4 \times 10.4 = 41.6 \text{ cm}

For the length (L), we will arrange 3 candles in a column, thus: L=3×10.4=31.2 cmL = 3 \times 10.4 = 31.2 \text{ cm}

Thus, the minimum dimensions of the box are 41.6 cm in length and 31.2 cm in width.

Step 2

Determine the number of candles he will be able to decorate with a 20-meter long ribbon.

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Answer

Start by calculating the total length of ribbon needed for one candle: Ribbon needed for one candle (cm) is given by the formula:
R=2×3,142×5.2+3=35.6768 cmR = 2 \times 3,142 \times 5.2 + 3 = 35.6768 \text{ cm}

Converting the total ribbon available: 20 meters is equal to 2000 cm.

To find the number of candles that can be decorated: Number of candles=200035.6768≈56.0\text{Number of candles} = \frac{2000}{35.6768} \approx 56.0

This means that 56 candles can be decorated with the available ribbon.

Step 3

Calculate the volume of wax needed for one horsehead candle.

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Answer

The volume of a cylindrical candle filled with wax is calculated using: V=3,142×(5.2)2×11.4V = 3,142 \times (5.2)^2 \times 11.4 First, calculate the volume:
V=3,142×27.04×11.4=968.54 cm3V = 3,142 \times 27.04 \times 11.4 = 968.54 \text{ cm}^3

Since the leftover wax fills 1/3 of the mould: Volume for horsehead=968.543≈322.85 cm3\text{Volume for horsehead} = \frac{968.54}{3} \approx 322.85 \text{ cm}^3

Thus, the volume of wax needed for one horsehead candle is approximately 322.85 cm³.

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