Justin has an injury that requires him to use a wheelchair for a while - NSC Mathematical Literacy - Question 2 - 2016 - Paper 1

First, we calculate the circumference of the rim using the formula:

$ext{Circumference} = ext{n} imes ext{diameter}$

where diameter = 584 mm, and n = 3.142:

$ext{Circumference} = 3.142 imes 584 ext{ mm} = 1834.94 ext{ mm}$

Next, the space occupied by the spokes:

$ext{Space filled by spokes} = 24 imes 2 ext{ mm} = 48 ext{ mm}$

Now, calculate the distance between the spokes:

ext{Distance between spokes} = rac{ ext{Circumference} - ext{space filled by spokes}}{24}

Substituting:

ext{Distance between spokes} = rac{1834.94 ext{ mm} - 48 ext{ mm}}{24} = 74.74 ext{ mm}

Thus, the distance between each spoke is 74.74 mm.

To find the available gap on both sides of the wheelchair, we first calculate the gap:

ext{Gap} = rac{750 ext{ mm} - 609.6 ext{ mm}}{2}

Calculating:

ext{Gap} = rac{750 - 609.6}{2} = rac{140.4}{2} = 70.2 ext{ mm}

Therefore, each side has an available gap of 70.2 mm.

To find the total width, we first convert the dimensions to meters. The total width is calculated as follows:

ext{Total Width} = rac{(80 + 640 + 80 + 640)}{1000} = rac{1440}{1000} = 1.44 ext{ m}

Thus, the total width of the two doors is 1.44 m.

We use the following formula:

e = rac{(80 + 640 + 95 + 220)}{2}

Calculating:

e = rac{1035}{2} = 517.5 ext{ mm}

Therefore, the value of e is 517.5 mm.

The total area for the rectangular glass panel can be calculated using:

ext{Total Area} = (640 imes 220) + 2 imes rac{(3.142 imes (95/2)^2)}{4}

Calculating areas:

$= 140800 + 2 imes 713.875 = 140800 + 1427.75 = 142227.75 ext{ mm}^2$

Thus, the total area is approximately 142227.75 mm^2.

The mass can be calculated using:

$ext{Total Mass} = ext{Volume} imes ext{Density}$

Substituting:

$ext{Total Mass} = 15985408 ext{ cm}^3 imes 2.5 ext{ g/cm}^3 = 39963520 ext{ g}$

Converting to kg:

ext{Total Mass} = rac{39963520}{1000} = 39963.52 ext{ kg}

Thus, the total mass of the glass panels is 39.96 kg.