Changing an arched window
8 written marks
A window consists of a rectangle of width \(10\) cm topped externally by a semicircle of diameter \(10\) cm. Its outside perimeter is \(30+5\pi\) cm. Let the rectangle height be \(h\).
Part a · 3 marks
Find \(h\) and the total window area.
Part b · 2 marks
A similar window has four times the area. Find its outside perimeter.
Part c · 3 marks
Return to the original window. Increase its rectangular height by \(3\) cm, but keep its original outside perimeter by changing the semicircle radius and the rectangle width together. Find the new radius exactly.
Complete-answer checking, worked solutions and indicative written criteria.
Open the complete answer form