Final answer:
Victoria will need approximately 122.46 square feet of paving for the walkway around her garden, calculated by determining the area of the two concentric circles and subtracting the smaller from the larger.
Step-by-step explanation:
To find out the area of the walkway that Victoria needs to pave, we first calculate the area of the outer circle with the walkway included and then subtract the area of the inner circle (the circular garden). The diameter of the garden is 10 feet, which makes its radius 5 feet. For the outer circle that includes the walkway, we add the width of the walkway (3 feet) to the radius of the garden (5 feet) which gives us a new radius of 8 feet.
The formula for the area of a circle is \( A = \pi r^2 \).
The area of the inner circle (garden) is:
- \( A_{inner} = \pi \times 5^2 = 25\pi \) square feet.
The area of the outer circle (garden plus walkway) is:
- \( A_{outer} = \pi \times 8^2 = 64\pi \) square feet.
The area of the walkway is the difference between the outer circle and the inner circle:
- \( A_{walkway} = A_{outer} - A_{inner} = 64\pi - 25\pi = 39\pi \) square feet.
Now we can approximate \( \pi \) as 3.14 to find the numerical value:
- \( A_{walkway} = 39 \times 3.14 \approx 122.46 \) square feet.
Therefore, Victoria will need approximately 122.46 square feet of paving for the walkway.