To help Gregory with his vegetable garden, we need to calculate two things:

1. The circumference of the garden: This will tell us how much fencing is needed.
2. The area of the garden: This will tell us how much fertilizer is needed.

1. Circumference of the Garden

The formula for the circumference $C$ of a circle is:

$C = \pi \times d$

Where $d$ is the diameter of the circle, and $\pi$ is approximately 3.1416.

Given:

• Diameter $d = 30$ meters

Thus:

$C = \pi \times 30 \approx 3.1416 \times 30 \approx 94.248 \text{ meters}$

So, Gregory will need about 94.25 meters of fencing to enclose the garden.

2. Area of the Garden

The formula for the area $A$ of a circle is:

$A = \pi \times r^2$

Where $r$ is the radius of the circle, and $\pi$ is approximately 3.1416. The radius $r$ is half of the diameter:

$r = \frac{d}{2} = \frac{30}{2} = 15 \text{ meters}$

Thus:

$A = \pi \times 15^2 = 3.1416 \times 225 \approx 706.86 \text{ square meters}$

So, Gregory will need enough fertilizer to cover an area of about 706.86 square meters.

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Would you like further details on these calculations or have any additional questions? Here are some related questions:

1. How do you calculate the area and circumference of a circle with a known radius?
2. What is the difference between diameter and radius, and how does it affect the formulas?
3. How would the calculations change if Gregory's garden were oval-shaped instead of circular?
4. What other factors should Gregory consider when choosing fencing and fertilizer?
5. What is the relationship between the radius, diameter, and circumference in a circle?

Tip: Always remember that the radius is half of the diameter—it's key to most circle-related formulas!