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: $A = \pi r^2$, where $\pi = 3,142$ Total surface area = $2\pi r^2 + 2 \pi rl$ Volume of the cylinder = $\pi r^2l$ 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 $\text{m}^2$. 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 cardboard. 2.2 Thabo discovered that his tap was faulty and has been leaking water at a rate of one drop every 2 seconds. The water that was wasted, was at a liver of 1 ml. Note: 1 kL = 1 000 mL; 1 mL = 1 000 000 microlitres. 2.2.1 Calculate the number of drops of water that filled a litre container. Use the formula: Number of drops = $\frac{Seconds \ in \ hour \ times \ number \ of \ hours}{rate \ of \ drops}$. 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 find the total surface area (SA) of the cylindrical container, use the formula:

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

Given the diameter (d) is 90 mm, the radius (r) is: $r = \frac{d}{2} = \frac{90 mm}{2} = 45 mm$

Converting this to meters: $r = \frac{45}{1000} = 0.045 m$

The length (l) of the cylinder is given as 270 mm, which converts to: $l = \frac{270}{1000} = 0.27 m$

Now plug the values into the surface area formula:

$SA = 2 \times 3.142 \times (0.045)^2 + 2 \times 3.142 \times (0.045) \times (0.27)$

Calculating: $SA ≈ 0.0127 + 0.0243 = 0.0370 m^2$

So, the total surface area of the cardboard package required is approximately $0.0370 m^2$ .

Step 2

2.1.2 Work out the area of the rectangular cardboard in m².

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Answer

The area (A) of a rectangle is calculated using the formula:

$A = length \times width$

Given dimensions of the cardboard are:

Length = 120 cm, which is $1.2 m$
Width = 60 cm, which is $0.6 m$

Now calculate:

$A = 1.2 m \times 0.6 m = 0.72 m^2$

Thus, the area of the rectangular cardboard is $0.72 m^2$ .

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 cardboard.

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Answer

From QUESTION 2.1.1, the total surface area of one cylindrical container is approximately $0.0370 m^2$ . From QUESTION 2.1.2, the area of the rectangular cardboard is $0.72 m^2$ .

To find the number of cylindrical containers (N) that can be made, use:

$N = \frac{Area \ of \ cardboard}{Total \ surface \ area \ of \ one \ container} = \frac{0.72}{0.0370} ≈ 19.46$

Therefore, Thabo can make approximately 19 containers.

Step 4

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

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Answer

To calculate the number of drops in one litre, we first need to find the total seconds in an hour and the drops per second:

Number of drops is given by:

$Number \ of \ drops = \frac{Seconds \ in \ hour \ times \ number \ of \ hours}{rate \ of \ drops}$

In one hour:

Seconds in an hour = 3600 s
Since one drop occurs every 2 seconds:
Rate of drops = $\frac{3600 s}{2} = 1800 drops$ .

Thus, for 1 litre (1000 mL):

As one drop is equal to 1 mL, there are 1000 drops in 1 litre.

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 in microlitres, we use the total number of drops from QUESTION 2.2.1:

$1 \ drop = 1 \ mL \ = 1000 \ microlitres$

Thus, the volume of one drop of water is $1000 \ microlitres$ .

Step 6

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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Answer

To find the total amount of water wasted:

Calculate the total number of days from 01/01/2016 to 31/05/2016:

There are 31 January days, 29 February days (2016 is a leap year), 31 March days, 30 April days, and 31 May days.
Total days = 31 + 29 + 31 + 30 + 31 = 152 days.

Calculate volume wasted:

Given the rate is 1 mL per drop and number of drops per day:
- $Volume = 152 \ days \times 24 \ hours/d \times 60 \ minutes/h \times 60 \ seconds/m \div 2 \ seconds/drop \times 1 \ mL/drop$

Convert this to litres: $Volume/(1000) L = (volume in mL) \div 1000$

Calculating gives us the total volume wasted in litres.

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 m².

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 cardboard.

2.2.1 Calculate the number of drops of water that filled a litre 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. Give your answer in litres.

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