Question

Victoria is paving a walkway around a circular garden with a diameter of 10 feet. If she wants the walkway to have a width of 3 feet, how many square feet of walkway will she need to pave?

a) 90π square feet
b) 120π square feet
c) 150π square feet
d) 180π square feet

Answer 1

To find the area of the walkway around a circular garden, subtract the area of the garden from the area of the larger circle formed by the walkway.

Step-by-step explanation:

To find the area of the walkway, we need to subtract the area of the circular garden from the area of the larger circle formed by the walkway. The radius of the circular garden is half the diameter, so it is 5 feet. The radius of the larger circle is the sum of the radius of the garden and the width of the walkway, which is 5 + 3 = 8 feet. The area of the walkway is then given by:

Area = π * (radiuslarger circle)2 - π * (radius)2

Area = π * (82 - π * (52))

Simplifying this, we get Area = π * (64 - 25) = π * 39.

Therefore, the amount of walkway Victoria will need to pave is 39π square feet.