Question

Kelsey has designed the pendant shown, 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. Part A 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. Then find the height rounded to the nearest tenth of a centimeter. Use 3.14 for π.

Answer 1

Answer:

$\dfrac{14}{\pi}\ \text{cm}$

4.5 cm

Step-by-step explanation:

If a straight line is bent into the shape of the circle the circumference of the circle will be equal to the straight line.

First circle's circumference is given by

$\pi d_1=6\\\Rightarrow d_1=\dfrac{6}{\pi}$

Second circle's circumference is given by

$\pi d_2=8\\\Rightarrow d_1=\dfrac{8}{\pi}$

Total height of the pendant

$d_1+d_2=\dfrac{6}{\pi}+\dfrac{8}{\pi}=\dfrac{14}{\pi}$

In terms of $\pi$ the height of the pendant is $\dfrac{14}{\pi}\ \text{cm}$

The height of the pendant is $\dfrac{14}{3.14}=4.5\ \text{cm}$