What is a circle?

​How would you describe a circle to someone who has never seen on before?

What is a circle?

​We can describe a circle mathematically. There are formulas we can use to determine the dimensions of any circle or circular shape. Today, we will learn some of the basic ones.

​Circles have parts

• A line across the center of the circle, from edge to edge is the diameter.

• A line from the center to the edge is the radius.

• The distance around the circle is the circumference.

92: Circumference, area and pi

The circumference of a circle requires us to calculate with the number pi. You might have learned pi as 3.14 or the symbol π.

In fact, π is infinite. It never repeats. This means that technically we can not ever get an EXACT measurement for the area or circumference of a circle because we are always rounding pi to just a few decimals.

Finding the circumference

C=2πr
C=dπ

If we are given the radius or diameter then we can easily solve for C.

Finding the Area

A=πr^{2
We can find the area of a circle if we are given the radius, circumference, or diameter.}

Example problem

Find the area of a circle with circumference 47.98cm.

1. We know we need the radius for the Area equation, so we first need to figure out the radius, which we can do because we have the circumference. C=2πr.
47.98=2*π*r
Dividing both sides of the equation by 2π leaves us with ~7.64=r

Example problem

Find the area of a circle with circumference 47.98cm.

2. We now know the radius (7.64), so our next step is to find the Area using the Area equation. A=πr²
Substitute 7.64 for r and square it (7.64*7.64). Then multiply by pi.
A=183.37 cm²

93: An introduction to volume

Volume is the amount of cubes measuring 1x1x1 units that will fit into a space. Some geometric solids are easier to calculate than others.

Rectangular prisms and Cubes are easy to calculate: Length*Width*Height.

Spheres, Cylinders, Pyramids and Tetrahedrons are also geometric solids, but have more complex equations for finding their volumes.

Triangular prism vs Pyramid vs Tetrahedron

Homework:

Lessons 91-93 & Ch 14 test.

Math lab 2:30-3:30 in Google Meet