Question

1. kelsey has designed a pendant, shown here, that hangs from a chain.

she makes pendants by bending silver wire into circles. the design connects one circle made from a wire 6 cm long to a second circle made from a wire 8 cm long.
she plans to sell the pendants at a craft fair, and her goal is to make a minimum profit of $50 at the fair.
the height of the pendant is determined by using the formula for the circumference of a circle, c = πd. find the total height of the pendant design from top to bottom in terms of π.
find the height rounded to the nearest tenth of a centimeter. use 3.14 for π. justify your answer.

Explanation:

Step1: Find the diameter of the first circle

The formula for the circumference of a circle is \(C=\pi d\). Given \(C = 6\) cm. Solving for \(d\), we get \(d=\frac{C}{\pi}=\frac{6}{\pi}\) cm.

Step2: Find the diameter of the second circle

Given \(C = 8\) cm. Using \(d=\frac{C}{\pi}\), we have \(d=\frac{8}{\pi}\) cm.

Step3: Calculate the total height (sum of diameters)

The total height \(h\) of the pendant is the sum of the diameters of the two circles. So \(h=\frac{6}{\pi}+\frac{8}{\pi}=\frac{6 + 8}{\pi}=\frac{14}{\pi}\) cm (in terms of \(\pi\)).

Step4: Calculate the numerical value

Using \(\pi=3.14\), \(h=\frac{14}{3.14}\approx4.5\) cm.

Answer:

In terms of \(\pi\), the height is \(\frac{14}{\pi}\) cm. Rounded to the nearest tenth, the height is \(4.5\) cm.