CUET · MATHS · PYQ PAPER 2023
The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.
If \(x\) and \(y\) represent the length and breadth of rectangular region, then the area A of the window in terms of \(x\) is :
- A \(A =x-\frac{\pi x^3}{8}-\frac{x^2}{2}\)
- B \(A =5 x-\frac{x^2}{2}-\frac{\pi x^2}{8}\)
- C \(A =5 x-\frac{x^2}{2}-\frac{3 x^2}{8}\)
- D \(A =5 x+\frac{x^2}{2}+\frac{\pi x^2}{8}\)
Answer & Solution
Correct Answer
(B) \(A =5 x-\frac{x^2}{2}-\frac{\pi x^2}{8}\)
Step-by-step Solution
Detailed explanation
\(P = 2y + x + \frac{\pi x}{2}\) \(10 = 2y + x + \frac{\pi x}{2}\) \(2y = 10 - x - \frac{\pi x}{2}\) \(y = 5 - \frac{x}{2} - \frac{\pi x}{4}\) \(A = xy + \frac{1}{2} \pi \left(\frac{x}{2}\right)^2\) \(A = x\left(5 - \frac{x}{2} - \frac{\pi x}{4}\right) + \frac{\pi x^2}{8}\)…
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