Question

6 an artist painted a circle on the side of a building that had a radius of 14 inches. what is the area that the artist painted in square inches? round to the nearest hundredth.
7 a horse pen is circular and has a radius of 15 feet. what is the area of the horse pen in square feet? round to the nearest hundredth.

Explanation:

Problem 6:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Substitute the given radius into the formula

Given that the radius \( r = 14 \) inches. Substitute \( r = 14 \) into the formula: \( A=\pi\times(14)^2 \)

Step3: Calculate the value

First, calculate \( 14^2 = 196 \). Then, \( A=\pi\times196\approx3.14159\times196 \)
\( 3.14159\times196 = 615.75204 \)

Step4: Round to the nearest hundredth

Rounding \( 615.75204 \) to the nearest hundredth gives \( 615.75 \)

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Substitute the given radius into the formula

Given that the radius \( r = 15 \) feet. Substitute \( r = 15 \) into the formula: \( A=\pi\times(15)^2 \)

Step3: Calculate the value

First, calculate \( 15^2 = 225 \). Then, \( A=\pi\times225\approx3.14159\times225 \)
\( 3.14159\times225 = 706.85835 \)

Step4: Round to the nearest hundredth

Rounding \( 706.85835 \) to the nearest hundredth gives \( 706.86 \)

Answer:

The area of the circle painted by the artist is approximately \( 615.75 \) square inches.

Problem 7: