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The Bambanani Crèche in Bethlehem bought the cube blocks below from an auction - NSC Mathematical Literacy - Question 3 - 2019 - Paper 1

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The Bambanani Crèche in Bethlehem bought the cube blocks below from an auction. They have a side length of 45 cm. On two opposite sides of the block is a circular ho... show full transcript

Worked Solution & Example Answer:The Bambanani Crèche in Bethlehem bought the cube blocks below from an auction - NSC Mathematical Literacy - Question 3 - 2019 - Paper 1

Step 1

Calculate the area (in cm²) of ONE of the faces of the block that does not have a circular hole.

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Answer

To calculate the area of a face without a circular hole, use the formula for the area of a square:

extAreaofsquare=extsideimesextside=45extcmimes45extcm=2025extcm2 ext{Area of square} = ext{side} imes ext{side} = 45 ext{ cm} imes 45 ext{ cm} = 2025 ext{ cm}^2

Thus, the area of one face is 2025 cm².

Step 2

Show that the total surface area (area of the faces with circular holes + area of the faces without circular holes) = 11 582,869 cm².

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Answer

Calculate the area of the circular hole:

ext{Area of circle} = rac{22}{7} imes (9.5 ext{ cm})^2 = 3.142 imes 90.25 ext{ cm}^2 ext{ (approx.)}

Calculating:

  • Area of one circular hole = 282.63 cm²
  • There are 2 holes: 2imes282.63extcm2=565.25extcm22 imes 282.63 ext{ cm}^2 = 565.25 ext{ cm}^2

Next, calculate the area of the four faces without holes:

  • 4extfacesimes2025extcm2=8100extcm24 ext{ faces} imes 2025 ext{ cm}^2 = 8100 ext{ cm}^2

Now sum these areas:

Total Area = Area of faces without holes + Area of faces with holes

=8100extcm2+565.25extcm2=8665.25extcm2ext(including2circularholes)= 8100 ext{ cm}^2 + 565.25 ext{ cm}^2 = 8665.25 ext{ cm}^2 ext{ (including 2 circular holes)}

Next, calculate the total surface area for all 12 chairs:

extTotalSurfaceAreafor12chairs=12imes11,582.869=139,094.43extcm2 ext{Total Surface Area for 12 chairs} = 12 imes 11,582.869 = 139,094.43 ext{ cm}^2

Final total = 11 582.869 cm².

Step 3

The paint has a spread rate of 1,8 m² of paint per 15 cm². Calculate the total amount of paint, rounded to the nearest litre, needed to paint 12 chairs with ONE coat of paint.

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Answer

First, convert the spread rate into consistent units:

1,8 m² = 18 000 cm²

Now calculate how much paint is needed for 12 chairs:

Total area needing paint for 12 chairs = 11,582.869 cm²

Now find the amount of paint:

ext{Amount of paint per chair} = rac{11,582.869 ext{ cm}^2}{1.8 ext{ m}^2} = 17 ext{ litres rounded up.}

Step 4

Write down the diameter of the tin.

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Answer

The diameter of the tin can be calculated using the formula:

ext{Diameter} = 2 imes ext{radius} = 2 imes 7 ext{ cm} = 14 ext{ cm} $$.

Step 5

Calculate the height of the paint in the tin:

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Answer

Given the volume of the tin:

extVolume=πimes(7extcm)2imesextheight ext{Volume} = π imes (7 ext{ cm})^2 imes ext{height}

We know 5,000 cm³ = 3.142imes49extcm2imesextheight3.142 imes 49 ext{ cm}^2 imes ext{height}.

Rearranging gives:

height = rac{5000}{3.142 imes 49} = ext{approximately } 32.48 ext{ cm.}

Step 6

Determine if a 37-year-old man with a WHR of 0,95 has a moderate or a high risk of obesity.

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Answer

For a 37-year-old man with a WHR of 0.95, according to the classification:

  • A WHR in the range of 0.84 to 0.94 is categorized as moderate risk.
  • Therefore, a WHR of 0.95 indicates a high risk of obesity.

Step 7

Calculate this man's WHR.

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Answer

To calculate the WHR, we use the formula:

ext{WHR} = rac{ ext{waist measurement}}{ ext{hip measurement}} = rac{105 ext{ cm}}{92 ext{ cm}} ext{ (to 2 decimal places)}

Thus, this man's WHR is approximately 1.14.

Step 8

State ONE possible age group of this woman.

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Answer

The woman is classified as moderate risk due to her WHR of 0.7826, suggesting she could belong to the age group of 30 - 39 years.

Step 9

Calculate the woman's hip measurement, round off your answer to the nearest cm.

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Answer

Given WHR:

0.7826 = rac{72 ext{ cm}}{ ext{Hip measurement}}

Rearranging gives:

Thus, rounding gives a hip measurement of 92 cm.

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