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During winter many children develop coughs - NSC Mathematical Literacy - Question 2 - 2019 - Paper 2

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During winter many children develop coughs. Cough syrups are sold in bottles packed in rectangular prism-shaped boxes. Children are given cough syrup using a cylindr... show full transcript

Worked Solution & Example Answer:During winter many children develop coughs - NSC Mathematical Literacy - Question 2 - 2019 - Paper 2

Step 1

Consider the cough syrup box. (a) Calculate (in cm³) the total surface area of the cough syrup box.

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Answer

To calculate the total surface area (SA) of the rectangular prism (cough syrup box), we apply the formula:

SA=2(l×w)+2(l×h)+2(w×h)SA = 2(l \times w) + 2(l \times h) + 2(w \times h)

Substituting in the values:

  • Length (l) = 6.5 cm
  • Width (w) = 6.5 cm
  • Height (h) = 12.5 cm
SA=2(6.5×6.5)+2(6.5×12.5)+2(6.5×12.5)=2(42.25)+2(81.25)+2(81.25)=84.5+162.5+162.5=409.5 cm2SA = 2(6.5 \times 6.5) + 2(6.5 \times 12.5) + 2(6.5 \times 12.5) = 2(42.25) + 2(81.25) + 2(81.25) = 84.5 + 162.5 + 162.5 = 409.5 \, \text{cm}^2

Thus, the total surface area of the cough syrup box is 409.5 cm².

Step 2

Consider the cough syrup box. (b) Give a practical reason why a cartoon picture would feature on the cough syrup box for children.

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Answer

A cartoon picture would feature on the cough syrup box to appeal to young children. It makes the medicine more attractive and engaging, promoting a positive association with the product, which can help in encouraging children to take their medicine.

Step 3

2.1.2 Calculate (in cm) the height of the medicine measuring cup if the diameter is 2,52 cm and the volume is 10 mL.

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Answer

First, we need to convert the volume from mL to cm³; since 1 mL = 1 cm³, the volume is 10 cm³. The volume (V) of a cylinder is given by:

V=π×r2×hV = \pi \times r^2 \times h

where the radius (r) can be calculated from the diameter (d):

r=d2=2.522=1.26 cm r = \frac{d}{2} = \frac{2.52}{2} = 1.26 \, \text{cm}

Now, substituting the known values into the volume formula:

10=3.142×(1.26)2×h10 = 3.142 \times (1.26)^2 \times h

Calculating the area:

(1.26)2=1.5876(1.26)^2 = 1.5876

Substituting:

10=3.142×1.5876×h10 = 3.142 \times 1.5876 \times h

Now, calculate the right-hand side:

10=4.94×h10 = 4.94 \times h

Solving for h:

h=104.94≈2.02 cmh = \frac{10}{4.94} \approx 2.02 \, \text{cm}

Therefore, the height of the measuring cup is approximately 2.02 cm.

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