# The area of a circle is 16pi. What is the circumference of the circle?

The area of a circle is

So we are given:

#pir^2 = 16pi#

Dividing both sides by

Then the circumference of a circle is

#2pir = 2*pi*4 = 8pi#

Footnote

Why is the circumference and area of a circle given by these formulas?

First note that all circles are similar and hence the ratio of the circumference to the diameter is always the same. We call that ratio, which is approximately

To see that the area of a circle is

This approximation gets better the more segments you have, but here's an animated illustration I put together...

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The circumference of the circle is 8π.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #5 # and the height of the cylinder is #7 #. If the volume of the solid is #42 pi#, what is the area of the base of the cylinder?
- A triangle has two corners with angles of # pi / 4 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #2 #, what is the largest possible area of the triangle?
- The base of a triangular pyramid is a triangle with corners at #(1 ,2 )#, #(5 ,2 )#, and #(7 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
- A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #2 #, its base has sides of length #1 #, and its base has a corner with an angle of #(3 pi)/8 #. What is the pyramid's surface area?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #3 # and #9 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?

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