Lesson 5 - Area of a Circle #6

[One speaker] 

[Video begins with a white screen that has the following words written at the top: “A cellphone tower has the ability to provide service to a circular region with a radius of 40.3 miles. Find the total surface area of the coverage zone. Round to the nearest hundredth.”]

Instructor: A cellphone tower has the ability to provide service to a circular region with the radius of forty point three miles. Find the total surface area of the coverage zone. Round to the nearest hundredth. So here’s a visual representation of what this might look like. [a gray circle appears that has a blue dot in the center along with a blue line that goes from the dot to the end of the circle] We have our cell tower in the middle, and we know that it can reach forty point three miles away. So, it can cover this whole region. [writes “40.3 mi” on the line within the circle] It asks us to find the surface area of the coverage zone.

So, we want to find the area of this circle formed by our coverage zone. We know that the area is found by pi R squared. [writes “A = π r^2” on the screen] In this case, our radius we were given is forty point three miles. So, our radius is forty point three miles. [writes “r = 40.3 mi” on the screen] So let’s plug that into our equation, and we can find the area. So we have pi times forty point three miles squared. [writes “” on the screen] 

Now, we can use our calculator. [pulls up calculator and inputs the equation] So forty point three squared equals one thousand six hundred twenty-four point zero nine. So let’s write that here: one thousand six hundred twenty-four point zero nine, and we have our miles squared. [writes “= π 1624.09 mi^2” on the screen] So miles squared, and let’s not forget that we have that times pi. So sometimes we might write that as 1624.09 pi miles squared, [writes 1624.09 π mi^2”] but if we want to multiply this out, we can go back to our calculator, [pulls up calculator] and we can multiply that by pi, and we get five thousand one hundred and two point two three if we were to round.

So five thousand one hundred and two point two three because it said to round to the nearest hundredth. But let’s not forget our miles squared. [writes “= 5102.23 mi^2” and draws a box around it] So, the area covered by the cell tower is five thousand one hundred and two point two three miles squared.

[End of Video]