The formula for finding an area of circle is equal to multiplied by the radius square

Question

Question for construction quiz

Answer 1

Hello Cassandra,

Here is a way you can remember the circle perimeter and circle area formulas. Take the time to make sure you understand this explanation, and you will always remember!

Supplies: One sheet of copy paper, scissors, tape, highlighter

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Part 1: The circumference or perimeter of a circle

The circumference is the same thing as the perimeter of a circle. We usually call it the circumference when referring to circles.

The copy paper dimensions are 8.5 inches by 11 inches.

1. Cut a strip of paper from the long side. Curve the edges together to form a circle. This circle has a perimeter of 11 inches.
2. Use tape to secure the edges. Don't overlap the edges: the perimeter should be 11 inches.
3. Now, compare the diameter of the circle to the 11-inch side of paper. What do you notice?
4. How many circles would be needed, to cover the full 11-inch side of paper?

O

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Notice that the circle's diameter is much shorter than the length of paper

How many circle diameters are needed to line up against the length of paper?

-- Three and a little bit more

-- Pi = 3.14159 ...

So, how can you find the perimeter of the circle?

-- The perimeter is also called the circumference

-- C = pi * diameter

Also, notice that

diameter = 2 * radius

Therefore,

-- C = pi * (2 * radius)

We have to use proper grammar, therefore, the equation is written in the following order:

-- C = 2 * pi * radius

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Part 2: The Area of a Circle

We are going to use the circumference formula, so make sure you understand the explanation above.

Imagine that you have a circle of flexible material. You can cut a radius of the circle and stretch it out. What is the shape it forms?

-- A triangle, with a very long base (C) and a short height (r)

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-- Base = Circumference

-- Height = radius

-- Area = 1/2 * base * height

-- Area = 1/2 * Circumference * radius

-- A = 1/2 * C * r

-- A = 1/2 * 2*pi*r * r substituting C = 2 * pi * r

-- A = 1 * pi * r^2 because 1/2 * 2 = 1

Therefore, the area of a circle = pi * r^2

Answer 2

Not certain exactly what you're asking, but for a circle with radius r, its area is π*r²