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Tshepo is renovating her home - NSC Mathematical Literacy - Question 3 - 2022 - Paper 2
Question 3
Tshepo is renovating her home. She is removing the wooden-framed windows and is replacing them with aluminium-framed windows. The dimensions and the shape of two of... show full transcript
Worked Solution & Example Answer:Tshepo is renovating her home - NSC Mathematical Literacy - Question 3 - 2022 - Paper 2
Step 1
Determine the perimeter of the rectangular window frame.
Answer
To find the perimeter of the rectangular window frame, we use the formula:
Given that the total length (A + B + C) is:
And the width is 149 cm. Thus, we calculate:
Therefore, the perimeter of the rectangular window frame is 716 cm.
Step 2
Calculate the inner area in cm² of the circular window frame.
Answer
To calculate the area of the circular window frame, we first need to find the radius from the inner diameter:
ext{Radius} = rac{ ext{Diameter}}{2} = rac{605 ext{ mm}}{2} = 302.5 ext{ mm} = 30.25 ext{ cm}Now, using the area formula for a circle:
Calculating the area gives:
Thus, the inner area of the circular window frame is approximately 2,872.07 cm².
Step 3
One of the windowpanes of the rectangular window frame broke. Write the probability, as a decimal, that it is NOT one of the windowpanes that can open.
Answer
In the rectangular window frame, there are four windowpanes, out of which four can open. Hence, there are no windowpanes that do not open.
The probability that it is NOT one of the windowpanes that can open is calculated as follows:
P( ext{NOT opening}) = rac{ ext{Number of non-opening panes}}{ ext{Total number of panes}} = rac{0}{4} = 0Therefore, the probability that it is NOT one of the windowpanes that can open is 0.0.