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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

Calculate (in cm²) the total surface area of the cough syrup box.

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Answer

To find the total surface area of the rectangular prism (cough syrup box), we use the formula:

Total Surface Area=2×(length×width)+2×(length×height)+2×(width×height)Total \, Surface \, Area = 2 \times (length \times width) + 2 \times (length \times height) + 2 \times (width \times height)

Substituting the given dimensions:

  • Length = 6.5 cm
  • Width = 6.5 cm
  • Height = 12.5 cm

Calculating:

  1. Calculate each term:

    • Length \times Width = 6.5 \times 6.5 = 42.25
    • Length \times Height = 6.5 \times 12.5 = 81.25
    • Width \times Height = 6.5 \times 12.5 = 81.25

  2. Substitute these values into the surface area formula:

Total Surface Area=2×42.25+2×81.25+2×81.25Total \, Surface \, Area = 2 \times 42.25 + 2 \times 81.25 + 2 \times 81.25
  1. Simplifying gives:
Total Surface Area=84.5+162.5+162.5=409.5 cm2Total \, Surface \, Area = 84.5 + 162.5 + 162.5 = 409.5 \, cm^2

So the total surface area of the cough syrup box is approximately 409.5 cm².

Step 2

Give a practical reason why a cartoon picture would feature on the box of cough syrup for children.

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Answer

A cartoon picture on the cough syrup box appeals to young children by making the product more attractive and engaging. This visual representation can make the medicine seem less intimidating, encouraging children to take it. Additionally, it can help parents choose the right medicine that is specifically designed for children, enhancing its appeal.

Step 3

Calculate (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

To find the height of the cylindrical measuring cup, we use the volume formula for a cylinder:

Volume=π×radius2×heightVolume = \pi \times radius^2 \times height

Given:

  • Diameter = 2.52 cm, so Radius = \frac{2.52}{2} = 1.26 cm
  • Volume = 10 mL, which is equivalent to 10 cm³

Substituting these values into the formula:

10=3.142×(1.26)2×height10 = 3.142 \times (1.26)^2 \times height

Calculating ( (1.26)^2 ):

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

Now substituting:

10=3.142×1.5876×height10 = 3.142 \times 1.5876 \times height

Dividing both sides by $ (3.142 \times 1.5876) $ to isolate height:

height=103.142×1.5876≈104.976≈2.01 cmheight = \frac{10}{3.142 \times 1.5876} \approx \frac{10}{4.976} \approx 2.01 \, cm

So the height of the cylindrical measuring cup is approximately 2.01 cm.

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