Question

1. a car wheel has a radius of 13 inches. what is the approximate circumference of the tire? (use 3.14 as an approximation for π)

a. 40.82 in.
b. 81.64 in.
c. 106.21 in.
d. 165.10 in.

1. what is the approximate area of a circle with a radius of 4 meters, rounding to the nearest tenth of a square meter? (use 3.14 for π)

a. 12.6 m²
b. 25.1 m²
c. 50.2 m²
d. 54.0 m²

1. the figure below shows three small circles, each with a diameter of 6 centimeters, inside a larger circle.

image of a large circle with three smaller circles inside, each with diameter 6 cm, arranged in a line
what is the area of the shaded part of the figure?
a. 72π square centimeters
b. 81π square centimeters
c. 94π square centimeters
d. 108π square centimeters

Explanation:

Step1: Find the radius of the large circle

The diameter of each small circle is \(6\) cm. The diameter of the large circle is \(6\times3 = 18\) cm. So the radius of the large circle \(R=\frac{18}{2}=9\) cm.

Step2: Find the radius of the small circle

The radius of each small circle \(r = \frac{6}{2}=3\) cm.

Step3: Calculate the area of the large circle

The area formula of a circle is \(A=\pi R^{2}\). Using \(\pi = 3.14\), the area of the large circle \(A_{1}=3.14\times9^{2}=3.14\times81 = 254.34\) \(cm^{2}\).

Step4: Calculate the area of one small circle

Using the area formula \(A=\pi r^{2}\), with \(r = 3\) cm and \(\pi=3.14\), the area of one small circle \(A_{2}=3.14\times3^{2}=3.14\times9 = 28.26\) \(cm^{2}\).

Step5: Calculate the area of three small circles

The area of three small circles \(A_{3}=3\times A_{2}=3\times28.26 = 84.78\) \(cm^{2}\).

Step6: Calculate the area of the shaded part

The area of the shaded part \(A=A_{1}-A_{3}\). \(A = 254.34-84.78=169.56\) \(cm^{2}\). If we use the formula \(A=\pi(R^{2}-3r^{2})\), \(R = 9\), \(r = 3\), \(A=\pi(81 - 27)=54\pi\) \(cm^{2}\).

Answer:

C. \(54\pi\) square centimeters