Before you read

Answer first — the lesson below explains it.

A circular garden has a diameter of 14 feet. What area of soil is needed to fill it?

A
$7 π$
B
$14 π$
C
$49 π$
D
$196 π$

Check your answer

Answer:

Before you read

Answer first — the lesson below explains it.

A circular running track has radius 50 m. How far does a runner travel in 3 complete laps?

A
$100 π$ m
B
$150 π$ m
C
$300 π$ m
D
$7500 π$ m

Check your answer

Answer:

Theory

Circle Formulas

Circumference (perimeter of a circle):
$C = 2\pi r = \pi d$

Area:
$A = \pi r^2$

Key relationships: $d = 2r$ . $\pi \approx 3.14159...$

Circle with radius r and diameter 2r

Example 1

A circle has radius 7 cm. Find its circumference and area.

$C = 2\pi(7) = 14\pi \approx 43.98$ cm

$A = \pi(7)^2 = 49\pi \approx 153.94$ cm $^{2}$

C = 14\pi

A = 49\pi

Quick check

You just read it. Can you apply it?

A pizza maker doubles the radius of a pizza from $r$ to $2 r$ . By what factor does the pizza's area increase?

A
2
B
$2 π$
C
4
D
$4 π$

Check your answer

Answer:

$A = π r^{2}$ . If $r t o 2 r$ : $A^{'} = π (2 r)^{2} = 4 π r^{2} = 4 A$ . Area quadruples.

Strategy

SAT Pro Tip

Always check if the problem gives radius or diameter. This is the #1 error source on circle problems. If diameter is 10, radius is 5 — use 5 in the formulas!

After reading

Same question as before. What do you say now?

A circular garden has a diameter of 14 feet. What area of soil is needed to fill it?

A
$7 π$
B
$14 π$
C
$49 π$
D
$196 π$

Check your answer

Answer:

Radius $= 7$ . $A = π (7)^{2} = 49 π$ .

After reading

Same question as before. What do you say now?

A circular running track has radius 50 m. How far does a runner travel in 3 complete laps?

A
$100 π$ m
B
$150 π$ m
C
$300 π$ m
D
$7500 π$ m

Check your answer

Answer:

One lap $= 2 π (50) = 100 π$ m. Three laps $= 300 π$ m.

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