Question

independent practice
date ____ pa
ben and luna were asked
to find the area of a circle
with a diameter of 9 cm.
use their work to answer
the questions below.

ben
a = 3.14 (9)
a = 3.14 (81)
a = 254.34 cm²

luna
a = 3.14 (4.5²)
a = 3.14 (9)
a = 28.26 cm²

1. describe ben’s mistake in solving for the

area of the circle.

1. describe luna’s mistake in solving for the

area of the circle.

1. after identifying each of the mistakes that ben and luna made, find the correct area of the

circle. round your answer to the nearest hundredth.

Explanation:

Step1: Analyze Ben's error

Ben used diameter (9 cm) instead of radius in the area formula. The radius $r = \frac{9}{2} = 4.5$ cm, but he plugged 9 directly into $r^2$.

Step2: Analyze Luna's error

Luna correctly used radius $4.5$ cm, but miscalculated $4.5^2$. $4.5^2 = 20.25$, not 9.

Step3: Calculate correct area

Use the circle area formula $A = \pi r^2$. Substitute $\pi=3.14$, $r=4.5$ cm.
$A = 3.14 \times (4.5)^2 = 3.14 \times 20.25$
$A = 63.585 \approx 63.59$ cm²

Answer:

1. Ben used the circle's diameter (9 cm) instead of the radius when calculating the area.
2. Luna incorrectly calculated $4.5^2$ as 9 instead of 20.25.
3. Correct area of the circle: $\boldsymbol{63.59}$ cm²