Thabo bakes round biscuits known as-Rb for sale. He packs the biscuits in a cylindrical container made up of cardboard material. The diagram below shows the container and its dimensions. The diagram not drawn to scale. The following formulae may be used in answering the questions that follow. Area of the circle = $\pi r^2$, where $\pi = 3.142$ Total surface area = $2\pi r^2 + 2\pi rl$ Volume of the cylinder = $\pi r^2 l$ 2.1.1 Calculate the total surface area of the cardboard package required to make one cylindrical container. 2.1.2 The rectangular cardboard used to make the cylindrical containers, is bought at a price of R5 a piece measuring 120 cm by 60 cm. Work out the area of the rectangular cardboard in $\text{mm}^2$. 2.1.3 Use your answers in QUESTIONS 2.1.1 and 2.1.2 to determine the number of cylindrical containers that can be made from one piece of the cardboard. 2.2 Thabo discovered that his tap was faulty and has been leaking water drops at a rate of one drop every 2 seconds. The water that was wasted, was at a lave of: Note: 1 kL = 1 000 L; 1 L = 1 000 mL; 1 mL = 1 000 000 microlitres. 2.2.1 Calculate the number of drops of water that filled a liter container. Use the formula: Number of drops = $\frac{Seconds\ in\ an\ hour \ times\ number\ of\ hours}{rate\ of\ the\ drops}$ 2.2.2 Calculate the volume of one drop of water in microlitres. 2.2.3 Work out the amount of water wasted from 01/01/2016 to 31/05/2016. Give your answer in litres.

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Thabo bakes round biscuits known as-Rb for sale - NSC Mathematical Literacy - Question 2 - 2016 - Paper 1

Question 2

Thabo bakes round biscuits known as-Rb for sale. He packs the biscuits in a cylindrical container made up of cardboard material. The diagram below shows the containe... show full transcript

Worked Solution & Example Answer:Thabo bakes round biscuits known as-Rb for sale - NSC Mathematical Literacy - Question 2 - 2016 - Paper 1

Step 1

2.1.1 Calculate the total surface area of the cardboard package required to make one cylindrical container.

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Answer

To calculate the total surface area (SA) of the cylindrical package, we use the formula:

$SA = 2\pi r^2 + 2\pi rl$

First, we need to find the radius (r) from the diameter: $d = 90 \text{ mm} \Rightarrow r = \frac{d}{2} = \frac{90}{2} = 45 \text{ mm}$

Now, substituting the radius and the length (l = 270 mm) into the formula:

$SA = 2 \times 3.142 \times (45)^2 + 2 \times 3.142 \times 45 \times 270$

Calculating:

Area of the circular ends: $2 \times 3.142 \times 2025 = 12712.35$
Area of the curved surface: $2 \times 3.142 \times 45 \times 270 = 76035.60$

Therefore: $SA = 12712.35 + 76035.60 = 88747.95 \text{ mm}^2$

The total surface area of the cardboard package required is approximately $89,075.7 \text{ mm}^2$ .

Step 2

2.1.2 Work out the area of the rectangular cardboard in mm².

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Answer

To find the area of the rectangular cardboard, we use the formula:

$Area = length \times width$

Given:

Length = 120 cm = 1200 mm
Width = 60 cm = 600 mm

Substituting the values:

$Area = 1200 \times 600 = 720000 \text{ mm}^2$

Thus, the area of the rectangular cardboard is $720,000 \text{ mm}^2$ .

Step 3

2.1.3 Use your answers in QUESTIONS 2.1.1 and 2.1.2 to determine the number of cylindrical containers that can be made from one piece of the cardboard.

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Answer

To determine the number of cylindrical containers, we divide the area of the cardboard by the surface area of one container:

$\text{Number of containers} = \frac{Area\ of\ cardboard}{Total\ surface\ area\ of\ one\ container}$

Using the values:

Area of cardboard: 720000 mm²
Total surface area of one container: 89075.7 mm²

Thus: $\text{Number of containers} = \frac{720000}{89075.7} \approx 8.08$

Rounding down, Thabo can make 8 cylindrical containers.

Step 4

2.2.1 Calculate the number of drops of water that filled a liter container.

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Answer

To find the number of drops that fill a liter container, we can use the formula:

$\text{Number of drops} = \frac{3600 \text{ seconds/hour} \times 1 \text{ hour}}{2 \text{ seconds/drop}}$

Calculating this:

Number of drops: $\frac{3600 \times 1}{2} = 1800 \text{ drops}$

Therefore, the number of drops of water that filled a liter container is 1800 drops.

Step 5

2.2.2 Calculate the volume of one drop of water in microlitres.

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Answer

To find the volume of one drop of water, we can use the conversion from drops to microlitres:

$7200 \text{ drops} = 1 \text{ litre} = 1000 \text{ mL}$

Thus, $1 \text{ drop} = \frac{1000 \text{ mL} \times 1000 \text{ microlitres}}{7200} = 138.89 \text{ microlitres}$

The volume of one drop of water is approximately 138.89 microlitres.

Step 6

2.2.3 Work out the amount of water wasted from 01/01/2016 to 31/05/2016.

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Answer

To calculate the total water wasted over the specified period:

From 01/01/2016 to 31/05/2016 is 151 days.

Each drop corresponds to: $1 \text{ drop} = 138.89\text{ microlitres}$

Calculating the total drops in 151 days given 1800 drops/hour:

$151 \text{ days} \times 24 \text{ hours/day} \times 1800 \text{ drops/hour} = 6,525,600 \text{ drops}$

Calculating the total volume of water wasted: $Volume = 6,525,600 \text{ drops} \times 138.89 \text{ microlitres/drop} = 907,200,000 \text{ microlitres} = 912 \text{ L}$

Thus, $912$ litres of water were wasted.

Thabo bakes round biscuits known as-Rb for sale - NSC Mathematical Literacy - Question 2 - 2016 - Paper 1

Worked Solution & Example Answer:Thabo bakes round biscuits known as-Rb for sale - NSC Mathematical Literacy - Question 2 - 2016 - Paper 1

2.1.1 Calculate the total surface area of the cardboard package required to make one cylindrical container.

2.1.2 Work out the area of the rectangular cardboard in mm².

2.1.3 Use your answers in QUESTIONS 2.1.1 and 2.1.2 to determine the number of cylindrical containers that can be made from one piece of the cardboard.

2.2.1 Calculate the number of drops of water that filled a liter container.

2.2.2 Calculate the volume of one drop of water in microlitres.

2.2.3 Work out the amount of water wasted from 01/01/2016 to 31/05/2016.

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