Math  /  Geometry

QuestionThe circumference of a circular lot is 204 yards. What is the diameter of the lot? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. \square yards

Studdy Solution

STEP 1

1. The shape of the lot is a circle.
2. The circumference of the circle is 204 204 yards.
3. We need to find the diameter of the circle.

STEP 2

1. Recall the formula relating circumference and diameter.
2. Solve for the diameter using the given circumference.
3. Round the diameter to the nearest hundredth.

STEP 3

Recall the formula for the circumference of a circle:
C=π×d C = \pi \times d
where C C is the circumference and d d is the diameter.

STEP 4

Solve for the diameter using the given circumference:
204=π×d 204 = \pi \times d
To find d d , divide both sides by π \pi :
d=204π d = \frac{204}{\pi}

STEP 5

Calculate the diameter and round to the nearest hundredth:
Using π3.14159 \pi \approx 3.14159 ,
d2043.14159 d \approx \frac{204}{3.14159} d64.97 d \approx 64.97
The diameter of the lot is approximately:
64.97 yards \boxed{64.97} \text{ yards}

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