Question

dig deeper a circular oil spill has a radius of 2 miles. after a day, the radius of the oil spill increases by 3 miles. by how many square miles does the area of the oil spill increase? round to the nearest thousandth, if necessary.
the area increases by about □ square miles.

Explanation:

Step1: Find initial area

The formula for the area of a circle is $A = \pi r^2$. For initial radius $r_1=2$ miles:
$A_1 = \pi (2)^2 = 4\pi$

Step2: Find new area

New radius $r_2=2+3=5$ miles:
$A_2 = \pi (5)^2 = 25\pi$

Step3: Calculate area increase

Subtract initial area from new area:
$\Delta A = A_2 - A_1 = 25\pi - 4\pi = 21\pi$

Step4: Compute numerical value

Use $\pi \approx 3.14159$:
$\Delta A \approx 21 \times 3.14159 = 65.97339$

Answer:

65.973