Question

which of the following is closest to the radius of a circle that has an area equal to the area of the rectangle?
a rectangle has a length of 15 centimeters and a width of 8 centimeters.
which of the following is closest to the radius of a circle that has an area equal to the area of the rectangle?

○ 3 centimeters
○ 6 centimeters
○ 11 centimeters
○ 19 centimeters

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is the length and \( w \) is the width. Given \( l = 15 \) cm and \( w = 8 \) cm, so \( A = 15 \times 8 = 120 \) \( \text{cm}^2 \).

Step2: Set the area of the circle equal to the area of the rectangle

The formula for the area of a circle is \( A = \pi r^2 \). We know \( A = 120 \), so \( \pi r^2 = 120 \). Solving for \( r \), we get \( r^2=\frac{120}{\pi}\approx\frac{120}{3.14}\approx 38.22 \).

Step3: Find the radius

Take the square root of \( 38.22 \), \( r\approx\sqrt{38.22}\approx 6 \) cm (since \( 6^2 = 36 \) and \( 7^2 = 49 \), 38.22 is closer to 36, so the radius is closest to 6 cm).

Answer:

B. 6 centimeters