Question

dol given a set of problems, students will correctly solve problems involving the area of a circle in at least 4 of 5 questions.

1. a circle has an area of approximately 50.24 square centimeters. which measurement is closest to the radius of the circle in centimeters? use 3.14 for π.

a. 3 cm
b. 4 cm
c. 5 cm
d. 16 cm

1. the circle shown has a radius of 5 inches.

which measurement is closest to the area in square inches of the circle? use 3.14 for π.
a. 314 in²
b. 78.5 in²
c. 56.52 in²
d. 28.26 in²

1. raisa paints a tabletop that is shaped like a circle. the circumference of the table is 6π feet. what measurement is closest to the area of the tabletop in square feet? use 3.14 for π.

a. 18.84 ft²
b. 28.26 ft²
c. 37.68 ft²
d. 113.04 ft²

Explanation:

Problem 1

Step1: Recall the area formula of a circle

The formula for the area of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We know \( A = 50.24\space cm^{2}\) and \( \pi=3.14 \).

Step2: Substitute the known values into the formula

Substitute \( A = 50.24\) and \( \pi=3.14 \) into \( A=\pi r^{2} \), we get \( 50.24 = 3.14\times r^{2} \).

Step3: Solve for \( r^{2} \)

Divide both sides of the equation by \( 3.14 \): \( r^{2}=\frac{50.24}{3.14}=16 \).

Step4: Solve for \( r \)

Take the square root of both sides: \( r = \sqrt{16}=4\space cm \).

Step1: Recall the area formula of a circle

The formula for the area of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We know \( r = 5\space inches\) and \( \pi = 3.14 \).

Step2: Substitute the known values into the formula

Substitute \( r = 5\) and \( \pi=3.14 \) into \( A=\pi r^{2} \), we get \( A=3.14\times5^{2} \).

Step3: Calculate \( 5^{2} \)

\( 5^{2}=25 \).

Step4: Calculate the area

\( A = 3.14\times25 = 78.5\space in^{2} \).

Step1: Recall the circumference formula of a circle

The formula for the circumference of a circle is \( C = 2\pi r \) (or \( C=\pi d \)), where \( C \) is the circumference and \( r \) is the radius. We know \( C = 6\pi\space feet \).

Step2: Solve for the radius \( r \)

From \( C = 2\pi r \), substitute \( C = 6\pi \), we have \( 6\pi=2\pi r \). Divide both sides by \( 2\pi \), we get \( r=\frac{6\pi}{2\pi}=3\space feet \).

Step3: Recall the area formula of a circle

The formula for the area of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We know \( r = 3\space feet\) and \( \pi = 3.14 \).

Step4: Substitute the known values into the formula

Substitute \( r = 3\) and \( \pi = 3.14 \) into \( A=\pi r^{2} \), we get \( A=3.14\times3^{2} \).

Step5: Calculate \( 3^{2} \)

\( 3^{2}=9 \).

Step6: Calculate the area

\( A=3.14\times9 = 28.26\space ft^{2} \).

Answer:

B. 4 cm

Problem 2