Question

using the relationship between a circle’s circumference and diameter
solve each problem. show your work.
1 what is the radius of the circle?
circle with diameter 180 ft
2 what is the circumference of the circle? write your answer using π.
circle with diameter 10 cm
3 the diameter of a circle is 10 yards. find the approximate circumference of the circle, using 3.14 for π.
4 the radius of a circle is 15 inches. what is the circumference of the circle? write your answer using π.
5 the diameter of a circle is 24 feet. what is the approximate circumference of the circle? use 3.14 for π.
6 what is the exact circumference of a circle with diameter 48 millimeters?

Explanation:

Problem 1: What is the radius of the circle?

Step1: Recall the relationship between diameter (\(d\)) and radius (\(r\)): \(r=\frac{d}{2}\).

The diameter of the circle is given as 180 ft.

Step2: Calculate the radius.

\(r = \frac{180}{2}=90\) ft.

Step1: Recall the formula for the circumference (\(C\)) of a circle: \(C = \pi d\) (where \(d\) is the diameter).

The diameter of the circle is 10 cm.

Step2: Substitute the diameter into the formula.

\(C=\pi\times10 = 10\pi\) cm.

Step1: Recall the formula for the circumference (\(C\)) of a circle: \(C=\pi d\).

Here, \(d = 10\) yards and \(\pi\approx3.14\).

Step2: Substitute the values into the formula.

\(C = 3.14\times10=31.4\) yards.

Answer:

The radius of the circle is 90 feet.

Problem 2: What is the circumference of the circle? (Write your answer using \(\pi\))