Question

Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will not be used.

Answer 1

Bed A --- Third Option

Bed B --- Fifth Option

Explanation:

Flower Bed A)

The formula for circumference is:

`C=2\pi r`

The diameter of A is 10 feet. So, its radius is 5 feet.

Substitute 5 for r. So, the circumference of Bed A is:

`C=2\pi (5)=10\pi\text{ feet}`

The formula for the area of a circle is:

`A=\pi r^2`

Substitute 5 for r:

`A=\pi (5)^2`

Square and simplify:

`A=25\pi \text{ square feet}`

So, the circumference of Bed A is 10π feet and its area is 25π square feet.

Therefore, match Bed A to the third option.

Flower Bed B)

The radius of Bed B is 6 feet. Again, we can use the circumference and area formulas. Substitute 6 for r for circumference:

`C=2\pi (6)`

Multiply:

`C=12\pi\text{ feet}`

Substitute 6 for r for the area formula:

`A=\pi(6)^2`

Square and simplify:

`A=36\pi\text{ square feet}`

So, Bed B has a 12π feet circumference and a 36π square feet area.

Therefore, match Bed B to the fifth option.

And we're done!