Finding the Area of a Circle
The easiest way to find the area of a circle is to draw a circle on graph paper. Then count the number of squares or grids inside the circle. This method requires drawing the circle precisely on the lines to mimimize the number of partial squares and the need to count and add partial squares. The common way to find the area of a circle is to use a formula. A formula is a fact, rule or principle expressed in symbols. The formula to find the area of a circle is pi times radius times radius. The area of a circle is pi multiplied by the radius squared. A = pi x r x r.
Of course this makes everyone think of the old joke, But a pie are not square, a pie are round!
Every point in a circle is the same distance from the center of the circle. The distance from the center of the circle to the edge of the circle is called the radius. The length of a bicycle wheel spoke is the radius of the bicycle wheel. The diameter of the circle is twice the length of the radius of the circle. The diameter of the bicycle wheel spoke is two times the length of the wheel spoke.
How many times can the diameter go around a circle? How many times can two bicycle wheel spokes go around the bicycle tire? How many times can two radii go around a car tire? How many times can two radii go around a semi-truck tire? Is the answer the same every time, no matter how small or how big the tire is? The answer is yes and it is between 3 and 4 times. The diameter goes around a circle between 3 and 4 times or 3.14 times exactly. It takes 3.14 diameters to go around a circle. This number is called pi. With the discovery of calculators and computers pi is defined precisely as 3.141592654.
We can use the area of a circle formula to calculate the area of a round wall clock. Let us say that the wall clock measures 18 inches across. That means the wall clock has a diameter of 18 inches. The radius is half the diameter. The radius of the wall clock is 9 inches. The area of the clock face can be calculated by multiplying pi times the radius times the radius. The area of the 18 inch clock face is pi times 9 times 9 or 3.14 x 9 x 9.
The area of the clock face is 3.14 multiplied by 81 or 254.35 square inches.
We can use the same formula to find the area of the bottom of a round salt shaker. If the radius of the salt shaker is inch. A = 3.14 x 1 x 1 or 3.14 square inches.
We can use this formula to find the area of a watch face or to find the area of any size circle.