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

`(14)/(\pi)\ \text{cm}`

4.5 cm

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=(6)/(\pi)`

Second circle's circumference is given by

`\pi d_2=8\\\Rightarrow d_1=(8)/(\pi)`

Total height of the pendant

`d_1+d_2=(6)/(\pi)+(8)/(\pi)=(14)/(\pi)`

In terms of
`\pi` the height of the pendant is
`(14)/(\pi)\ \text{cm}`

The height of the pendant is
`(14)/(3.14)=4.5\ \text{cm}`