maximum surface area of rectangle with semi circles

Its approximate value, correct to 7 decimal places, is 3.1415927, but the decimal expansion of π continues forever with no apparent pattern. The number π is not a whole number, nor is it a rational number.

Since the diameter is twice the radius, we can also write Where C is the circumference and d is the diameter of the circle. Strictly speaking, a circle together with its interior is called a ‘disc’, but we generally use the word ‘circle’ to refer both to the circle and the disc. We use the term area of a circle to mean the area of the region contained within the circle.

This was first investigated by the Greeks who introduced the notion of a proportionality constant between the circumference and the diameter, to which we now give the symbol π (pi). Exactly how are the radius of a circle and its area related?Įxperimental evidence (using string) leads one to see that if the radius of a circle is doubled, then the circumference is doubled, and more generally that the circumference is proportional to the radius. Exactly how are the radius and circumference related?Ĭan we make sense of the area bounded by a circle in the same way that we define the area of a rectangle? Again it seems clear that the larger the radius of the circle, the larger the area. Clearly, the larger the radius of the circle, the greater the circumference. When a wheel is rolled in the sand through one revolution, what length is traced out? This length is the distance around the circle and is called the circumference of the circle. Lines and circles are thus fundamental in geometry. When we perform constructions, we use a ruler to draw a line and compasses to draw a circle. The circular wheel is widely regarded as one of mankind’s most important inventions. Coins, plates and tables are often in the shape of a circle, and racetracks generally have semi-circular ends, while fans move in circular motion. The circle is the most commonly seen figure whose boundary is not a straight line.

Maximum surface area of rectangle with semi circles