Question

1. a gardener prepares circular beds with a radius of 5 inches (shown in white in the figure) to plant hydrangeas. she sprays a pesticide around the beds in a strip 3 inches wide (shown in grey in the figure). what is the area of the ground that she sprays? a) 9π inches² b) 25π inches² c) 39π inches² d) 99π inches²

Explanation:

Step1: Recall area formula for circle

The area formula of a circle is $A = \pi r^{2}$, where $r$ is the radius of the circle.

Step2: Find radius of outer - circle

The radius of the inner - circle is $r_1=5$ inches and the width of the strip is 1 inch. So the radius of the outer - circle $r_2=r_1 + 1=5 + 1=6$ inches.

Step3: Calculate area of inner - circle

$A_1=\pi r_1^{2}=\pi\times5^{2}=25\pi$ square inches.

Step4: Calculate area of outer - circle

$A_2=\pi r_2^{2}=\pi\times6^{2}=36\pi$ square inches.

Step5: Calculate area of the grey strip

The area of the grey strip (the area to be sprayed) is $A = A_2−A_1$. Substitute $A_1 = 25\pi$ and $A_2 = 36\pi$ into the formula: $A=36\pi−25\pi = 11\pi$ square inches.

Answer:

$11\pi$ square inches