# Thread: Circular mirrors are expensive

1. ## Circular mirrors are expensive

The cost of a circular mirror is directly proportional to the square of the diameter.
A circular mirror with a diameter of 6cm costs $50. What is the cost of a circular mirror with a diameter of 90 cm? This is what I tried: If a 60cm mirror costs$50, then each cm is 50/60 = 0.83 per cm. Therefore, 90 * 0.83 = 75 cm. But this is wrong. Help.

PS how do I put up a graph question here? There doesn't seem to be a copy an attach or copy & paste function.

The cost of a circular mirror is directly proportional to the square of the diameter.
A circular mirror with a diameter of 6cm costs $50. What is the cost of a circular mirror with a diameter of 90 cm? This is what I tried: If a 60cm mirror costs$50, then each cm is 50/60 = 0.83 per cm. Therefore, 90 * 0.83 = 75 cm. But this is wrong. Help.

PS how do I put up a graph question here? There doesn't seem to be a copy an attach or copy & paste function.
This is how you set up a proportional problem. The letter "k" represents the constant of proportionality.

$C=kD^2$

Since we have that a 60cm mirror costs \$50, we can find "k" as:

$50 = k(60)^2$
$\Rightarrow k=50/3600=5/360=1/72$

Now we need to find the cost of a 90 cm mirror:

$C= \frac {1}{72}(90)^2 = \frac {1}{72}(8100) = \112.50$