Question

The floor of a birdcage is a circle with a circumference of about 47.1 inches. What is the diameter of the birdcage floor?.

Short answer

The diameter of birdcage is 15 inches.

Step-by-step solution

Step 1. Relation between the radius and circumference of a circle is.

The circumference C of a circle is equal to $2\pi$times its radius. That is, $C=2\pi r$.

Where r is the radius of circle.

Step 2. Calculate the radius of the birdcage floor.

To find the radius of the birdcage, use the above formula of circumference and substitute 47.1 for C and simplify further for r as shown below:

$\begin{array}{l}47.1=2\pi \left(r\right)\\ r=7.5\text{inches}\end{array}$

Step 3. Calculate the diameter of the birdcage floor.

Since the radius is half of the diameter, so to find the diameter of the birdcage, multiply the radius by 2 and solve further to get

$\begin{array}{l}d=2r\\ d=2\left(7.5\right)\\ d=15\text{inches}\end{array}$

Therefore, the diameter of the birdcage is 15 inches.