SSAT Middle Level

Circles

Q: Why do some questions ask for an 'approximate' answer?

Because `\pi` is a number that goes on forever (`3.14159...`), we usually use an estimate like `\frac{22}{7}` or `3.14` to make the math easier. When you use an estimate, your answer is approximate!

Q: How do I find the radius if I only know the diameter?

Just cut the diameter in half! If the diameter is `10`, the radius is `\frac{10}{2}`, which equals `5`.

Circumference, area, arcs, sectors, central angles, and radius/diameter — excludes composite shapes involving circles (see area-perimeter-composite)

Generate Unlimited Practice Questions

Start Free Practice

Learn This Topic

Have you ever tried to share a giant pepperoni pizza with your friends and wondered exactly how much cheese you're getting? 🍕 Welcome to the wonderful world of circles! On the SSAT, circles are one of the most popular geometry shapes you'll see. But don't worry, once you learn the secret 'pizza parts,' circle questions become a piece of cake (or a slice of pie!).

Let's break down the vocabulary. The center is the exact middle of the circle. The radius is a straight line from the center to the edge—think of it as the distance from the middle of your pizza straight to the crust. If you draw a line all the way across the pizza, passing right through the center, that's the diameter. Here's a cool trick: the diameter is always exactly twice as long as the radius! 🎡

Next up is the circumference. This is a fancy math word for 'perimeter' when we're talking about circles. It's the total length of the outside edge—the crust! Finally, the area is all the space inside the circle, which is where all the delicious cheese and toppings live. To solve SSAT circle problems, you'll use a special symbol called $π$ (pi). It sounds yummy, but it's actually just a magical math number that equals about $3.14$ or $\frac{22}{7}$ . Whenever you see a circle question on the test, just remember your pizza parts, and you'll do great! 🥧

Key Formula

The two most important formulas are for Area (the cheese) and Circumference (the crust). Area:

A = π \cdot r^{2}

. Circumference:

C = π \cdot d

C = 2 \cdot π \cdot r

Practice Questions

4 practice questions for SSAT Middle Level

Q1 Medium

If the circumference of a circle is

18 π

centimeters, what is the area of the circle in square centimeters?

9 π

18 π

36 π

81 π

324 π

Show Solution

The formula for the circumference of a circle is $C = 2 π r$ . If the circumference is $18 π$ , we can set up the equation $2 π r = 18 π$ . Dividing both sides by $2 π$ gives a radius of $r = 9$ centimeters. The formula for the area of a circle is $A = π r^{2}$ . Substituting $r = 9$ gives $A = π (9)^{2} = 81 π$ .

Answer: D

Q2 Medium

A unicycle wheel has a diameter of 20 inches. How far, in inches, will the unicycle travel if the wheel makes exactly 5 complete revolutions?

20 π

50 π

100 π

200 π

400 π

Show Solution

The distance the wheel travels in one complete revolution is equal to its circumference. The formula for circumference is $C = π d$ . Since the diameter $d = 20$ , the circumference is $20 π$ inches. For 5 revolutions, multiply the circumference by 5: $5 \times 20 π = 100 π$ inches.

Answer: C

Q3 Medium

A circle has a center at point

O

and a radius of 7. Which of the following could NOT be the length of a line segment connecting any two points on the circle?

A 5

B 7

C 12

D 14

E 16

Show Solution

The longest possible line segment connecting any two points on a circle is the diameter. The diameter is exactly twice the radius. Since the radius is 7, the diameter is $2 \times 7 = 14$ . Therefore, no line segment connecting two points on this circle can have a length greater than 14. Because 16 is greater than 14, it cannot be the length of such a segment.

Answer: E

Q4 Medium

A circular pizza has a radius of 6 inches. A smaller circular cutout with a radius of 2 inches is removed from the exact center of the pizza. What is the area, in square inches, of the remaining portion of the pizza?

8 π

16 π

32 π

36 π

40 π

Show Solution

To find the area of the remaining portion, subtract the area of the smaller cutout from the area of the original pizza. The area of a circle is $A = π r^{2}$ . The area of the original pizza is $π (6)^{2} = 36 π$ . The area of the cutout is $π (2)^{2} = 4 π$ . Subtracting the two areas gives $36 π - 4 π = 32 π$ square inches.

Answer: C

Tips & Strategies

Always double-check if the question gives you the radius or the diameter. It is the #1 trick the SSAT uses to catch you off guard!
Leave pi alone! Before you start doing messy math with $3.14$ , look at the answer choices. Often, the SSAT leaves $π$ right in the answer (like $10 π$ ), saving you lots of time.
If a question asks for a fraction of a circle (like a slice of pizza), find the whole area first, then multiply by the fraction. For example, half a pizza is $\frac{1}{2} \cdot π \cdot r^{2}$ .

Common Mistakes

Watch out for mixing up the Area and Circumference formulas! Remember: Area has a 'squared' in it ( $r^{2}$ ) because area is always measured in square units.
Don't forget the order of operations! When finding Area ( $A = π \cdot r^{2}$ ), you must square the radius FIRST, before multiplying by $π$ .

Frequently Asked Questions

What exactly is pi (

π

Pi is a special math number that shows how many times a circle's diameter fits around its outside edge. It fits a little more than 3 times, which is why it's approximately $3.14$ or $\frac{22}{7}$ !

Do I need to memorize the formulas for the SSAT?

Yes! The SSAT does not give you a formula sheet. You must memorize the formulas for Area, Circumference, and Diameter before test day.

Why do some questions ask for an 'approximate' answer?

Because $π$ is a number that goes on forever ( $3.14159...$ ), we usually use an estimate like $\frac{22}{7}$ or $3.14$ to make the math easier. When you use an estimate, your answer is approximate!

How do I find the radius if I only know the diameter?

Just cut the diameter in half! If the diameter is $10$ , the radius is $\frac{10}{2}$ , which equals $5$ .

Generate Unlimited Practice Questions

Learn This Topic

Practice Questions

Tips & Strategies

Common Mistakes

Frequently Asked Questions

Related Topics

More Geometry

Other Levels

Browse

Generate Unlimited Practice Questions