Question

practice using the relationship between a circles circumference and diameter
study the example showing how to find the circumference of a circle.
then solve problems 1 - 5.
example
a model of a circular pool is shown. what is the exact circumference of the pool?
you can use a formula to find the circumference of a circle.
the diagram shows that the diameter of the pool is 9 ft.
c = πd
= π·9
= 9π
using π gives an exact circumference. the circumference of the pool is 9π ft.
1 a. a circular dining room table top has a radius of 22 inches. what is the diameter of the table top?
b. what is the circumference of the table top? write your answer using π. show your work.
2 a circular coin has circumference 32π millimeters. will the coin fit through a slot that is 35 millimeters long? explain.
vocabulary
circumference the distance around the outside of a circle.
diameter the distance across a circle through the center.
pi (π) in a circle, the quotient circumference/diameter. common approximations are 3.14 and 22/7.
radius (of a circle) the distance from the center of a circle to any point on the circle.

Explanation:

Step1: Recall the formula for diameter

The formula for diameter \(d\) in terms of radius \(r\) is \(d = 2r\).

Step2: Substitute the given radius

Given \(r = 22\) inches. Substitute into the formula: \(d=2\times22\).

Step3: Calculate the diameter

\(d = 44\) inches.

Step4: Recall the formula for circumference

The formula for circumference \(C\) is \(C=\pi d\) (or \(C = 2\pi r\)). Since \(d = 44\) inches (from part a), use \(C=\pi d\).

Step5: Substitute the diameter into the circumference formula

\(C=\pi\times44\).

Step6: Write the final expression for circumference

\(C = 44\pi\) inches.

Step7: For the coin problem

Recall the formula \(C=\pi d\). Given \(C = 32\pi\) mm. Solve for \(d\): \(d=\frac{C}{\pi}\).

Step8: Substitute the circumference value

\(d=\frac{32\pi}{\pi}=32\) mm.

Step9: Compare the diameter with the slot length

The diameter of the coin \(d = 32\) mm and the slot length is \(35\) mm. Since \(32<35\).

Answer:

a. \(44\) inches
b. \(44\pi\) inches
For the coin problem: Yes, the coin will fit through the slot. Because the diameter of the coin \(d = 32\) mm (calculated from \(C=\pi d\) with \(C = 32\pi\) mm) and \(32<35\) (the length of the slot).