A Little More on Circles

Links and useful resources

• gr7's Prealgebra Course Outline START HERE<<<
• AoPS Online Textbook
• IXL Grade 7 index
• IXL Grade 8 index
• AoPS Alcumus
• IXL prealgebra practice index
• OpenSTAX Prealgebra-1 textbook

Concept summary and lesson

• Radius, Circumference, Area and PI
  • $\pi$ is the ratio of a circle's circumference to its diameter: $\pi =\frac{c}{d}$
  • Therefore, the circumference $c=\pi d=2\pi r$
  • The area of a circle is $\pi r^2$, which you can start to get an intuitive understanding of by looking at this diagram:

• Using $\frac{22}{7}$ for $\pi$
  • $\frac{22}{7}\approx 3.1428$, so it's a decent approximation to use for in-class problems where hundredths are basically always close enough.

Worked examples

• A farmer has a square lot that is 200 feet on each side. She has a very powerful sprinkler that sprays water in a circle. She doesn’t want to waste any water, so she’ll set her sprinkler so that it doesn’t spray any water outside her lot. What is the largest percentage of her lot that she can water? (Answer to the nearest whole percent.)

Guided practice

• If the diameter of a circular ring of mushrooms is 10 meters, what is its circumference? Use two-column format to answer the question.
• What is the area of ground enclosed by the mushroom ring?
• What is the area of a circle whose circumference is 50 inches?
• What is the circumference of a circle whose area is 100 square centimeters?
• A pizza slice that is one eighth of the total pizza weighs 200 grams. If you wanted to scale up the pizza so that the same slice weighed 300 grams, how much bigger would the diameter be for the new pizza? How much would you need to increase all of the toppings and other ingredients in the recipe?

Homework

• #hw (math) (gr7) IXL circles word problems 2025-03-14