Math / Geometry

QuestionThe circumference of a circular field is 200 yards. What is the diameter of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. $\square$ yards

Studdy Solution

STEP 1

1. The field is perfectly circular.
2. The circumference of the circle is $200$ yards.
3. The relationship between circumference and diameter is given by the formula $C = \pi \times d$ .

STEP 2

1. Recall the formula relating circumference and diameter.
2. Solve for the diameter.
3. Perform the calculation and round the result.

STEP 3

Recall the formula relating circumference and diameter:
$C = \pi \times d$

STEP 4

Solve for the diameter $d$ :
$d = \frac{C}{\pi}$

STEP 5

Substitute the given circumference into the formula and calculate:
$d = \frac{200}{\pi}$
Using the approximation $\pi \approx 3.14159$ , calculate:
$d \approx \frac{200}{3.14159}$ $d \approx 63.66$
Round the result to the nearest hundredth:
$d \approx 63.66$
The diameter of the field is:
$\boxed{63.66} \text{ yards}$

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