Question

8. Measurement Jillian measured the distance around a small fish pond to be 27 yards. What would be a good estimate of the distance across the pond: 14 yards, 9 yards, or 7 yards? Explain how you decided.

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Hester

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To estimate the distance across the pond, we can use the relationship between the distance around a pond (circumference) and the distance across the pond (diameter) in a circle.

The circumference of a circle can be calculated by the formula:

C = 2 \pi r

where C is the circumference and r is the radius.

In this case, we don't know the radius or the diameter of the pond, but we do know the circumference is 27 yards. So, we can set up the equation:

27 = 2 \pi r

To estimate the diameter, we need to find the value of r. We can do this by dividing both sides of the equation by 2 π:

r = \frac{27}{2 \pi}

To estimate the diameter, we can multiply the radius by 2:

d = 2r = 2 \left(\frac{27}{2 \pi}\right) = \frac{27}{\pi} \approx 8.6 \text{ yards}

Therefore, a good estimate of the distance across the pond would be 9 yards.

\textbf{Answer:} A good estimate of the distance across the pond would be 9 yards.

The circumference of a circle can be calculated by the formula:

where C is the circumference and r is the radius.

In this case, we don't know the radius or the diameter of the pond, but we do know the circumference is 27 yards. So, we can set up the equation:

To estimate the diameter, we need to find the value of r. We can do this by dividing both sides of the equation by 2 π:

To estimate the diameter, we can multiply the radius by 2:

Therefore, a good estimate of the distance across the pond would be 9 yards.

\textbf{Answer:} A good estimate of the distance across the pond would be 9 yards.

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