3.1 Simphiwe will pack 12 cylindrical candles in a box using a 4 by 3 arrangement. Determine the minimum length and width of the box he needs if the candles are tightly packed, touching each other in the box. 3.1.2 Simphiwe ties a decorative ribbon around the candles. The ribbon has an overlap of 3 cm. Determine the number of candles he will be able to decorate with a 20-meter long ribbon. You may use the following formula: Ribbon needed for one candle (cm) = 2 × 3,142 × radius + 3 3.1.3 After carving a horsehead in a cylindrical candle, he collected the leftover wax, melted it and poured it in the mould. The leftover wax filled up rac{1}{3} of the mould. Calculate the volume of wax needed for one horsehead candle. You may use the following formula: Volume of a cylinder = 3,142 × (radius)² × height

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3.1 Simphiwe will pack 12 cylindrical candles in a box using a 4 by 3 arrangement - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1

Question 3

3.1 Simphiwe will pack 12 cylindrical candles in a box using a 4 by 3 arrangement. Determine the minimum length and width of the box he needs if the candles are tig... show full transcript

Worked Solution & Example Answer:3.1 Simphiwe will pack 12 cylindrical candles in a box using a 4 by 3 arrangement - 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, we need to consider how the candles are arranged.

Each cylindrical candle has a diameter of $2 imes 5,2 ext{ cm} = 10,4 ext{ cm}$ . Therefore, the width of one candle is 10.4 cm.
Since there are 4 candles placed side by side, the total width will be:
$ext{Width} = 4 imes 10,4 ext{ cm} = 41,6 ext{ cm}$
Additionally, the height of the box needs to accommodate the candle height, which is 11.4 cm. Thus, the dimensions of the box must be at least 41.6 cm in width and 11.4 cm in height.

Step 2

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

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Answer

The calculation for the ribbon needed for one candle is as follows:

$ext{Ribbon needed for one candle} = 2 imes 3,142 imes 5,2 + 3 = 35,6768 ext{ cm}$
We convert the total ribbon length into centimeters:

$20 ext{ meters} = 2000 ext{ cm}$
To find the number of candles he can decorate, we divide the total ribbon by the ribbon length needed for one candle:

$ext{Number of candles} = \frac{2000 ext{ cm}}{35,6768 ext{ cm}} \\approx 56. ea\text{ (rounded down)}$

So, Simphiwe can decorate 56 candles.

Step 3

Calculate the volume of wax needed for one horsehead candle.

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Answer

First, we calculate the volume of the cylindrical candle using the given formula:

$ext{Volume} = 3,142 imes (5,2)^2 imes 11,4 \\approx 968,54 ext{ cm}^3$
The volume of wax remaining after making the horsehead is:

$ext{Volume of horsehead} = 968,54 - \frac{1}{3} \times 968,54 = 645,69 ext{ cm}^3$

Thus, the volume of wax needed for one horsehead candle is approximately 645.69 cm³.

3.1 Simphiwe will pack 12 cylindrical candles in a box using a 4 by 3 arrangement - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1

Worked Solution & Example Answer:3.1 Simphiwe will pack 12 cylindrical candles in a box using a 4 by 3 arrangement - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1

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

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

Calculate the volume of wax needed for one horsehead candle.

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