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ANNEXURE C shows the seating plan for a cinema during the Covid-19 pandemic - NSC Mathematical Literacy - Question 4 - 2022 - Paper 2
Question 4
ANNEXURE C shows the seating plan for a cinema during the Covid-19 pandemic. Seats marked with an 'X' need to be left vacant in order to comply with social distancin... show full transcript
Worked Solution & Example Answer:ANNEXURE C shows the seating plan for a cinema during the Covid-19 pandemic - NSC Mathematical Literacy - Question 4 - 2022 - Paper 2
Step 1
Step 2
Assume that pre-Covid-19 conditions apply and all the seats are occupied. (a) Name the row and seat number of the middle seat in the 8th row from the screen.
Answer
The middle seat in the 8th row can be found by determining the number of seats in that row. If there are 10 seats in total, the middle seat would be seat 5.
Step 3
Assume that pre-Covid-19 conditions apply and all the seats are occupied. (b) Write down the ratio of the number of wheelchair spaces to the number of seats for persons NOT in wheelchairs.
Answer
Assuming there are 4 wheelchair spaces and 130 total seats, the ratio would be 4:126, simplifying to 2:63.
Step 4
On Friday evenings, pre-Covid-19, all the seats in the cinema (excluding the wheelchair spaces) were always occupied. Calculate the percentage income lost due to social distancing during the pandemic if ALL the tickets for the seats are equally priced.
Answer
If there are 66 vacant seats due to social distancing, the percentage income lost can be calculated as follows:
Income lost = (Total vacant seats / Total seats) × 100
= (66 / 130) × 100 = 50.77%.
Step 5
Step 6
The steel used to make the tank is 5 mm thick all around. For safety reasons, the tank is filled to 95% of its capacity. (a) Show that the inner diameter of the tank is 3,21 m.
Answer
To find the inner diameter, subtract twice the thickness of the steel from the outer diameter:
Inner diameter = Outer diameter - 2 × thickness = 7.25 m - 2 × 0.005 m = 3.21 m.
Step 7
The steel used to make the tank is 5 mm thick all around. For safety reasons, the tank is filled to 95% of its capacity. (b) Calculate the maximum litres of diesel that this tank can hold according to safety regulations.
Answer
The volume of diesel that the tank can hold:
Volume = 3,142 × (1.605)² × 3.22 = 55,669.64 litres, accounting for the 95% capacity gives us: 55,669.64 × 0.95 = 52,886.15 litres.
Step 8
The external surface area of the tank, excluding the base area of the external attachments, needs to be painted. The spread rate of the paint is 3 m²/L. Verify, by showing all calculations, whether the manager is CORRECT.
Answer
First, calculate the surface area:
Surface area = 2 × 3.142 × (1.605) × (1.605 + 3.22) = 88.64 m².
The amount of paint needed: Total area to be painted = 88.64 - 1 = 87.64 m².
Thus, litres needed = 87.64 / 3 = 29.22 litres, which is less than 30 litres.