Question

a norman window consists of a rectangle surmounted by a semicircle. if the perimeter of a norman window is to be 32 feet, determine what should be the radius of the semicircle and the height of the rectangle such that the window will admit the most light.?4.49 ft.

Answer 1

Therefore, the height of the rectangle and the radius of the semicircle should be 8 feet each in order for the Norman window to admit the most light.

What is the perimeter of a semi circle?

The distance along the line defining a half circle's boundary is known as the semi circle's perimeter. It is made up of the diameter of the semi circle, which is a straight line that passes through the center of the circle, and the semi circle's curving arc. For example, he radius of the semicircle and the height of the rectangle such that the window will admit the most light. A semi circle's diameter must be determined before calculating the circumference. This may be accomplished by determining the radius of the semicircle, which is the separation between any two points on the circle and the circle's center. Simply said, the diameter is twice the radius.

How to solve?

If the perimeter of the Norman window is 32 feet, then each side of the rectangle must be 8 feet long. ( using 2(l+b))

The radius of the semicircle must also be 8 feet, as the perimeter of a semicircle is equal to 2 * pi * radius.

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