A circular oil spill is spreading over the surface of a

lake. The circle’s radius grows by 500 meters every hour.
How many square kilometers did the spill grow between
24 hours and 48 hours?

radius after 24 hrs

= 500(24) = 12000 m or 12 km
area after 24 hrs
= π(12)^2 = 144π square km

radius after 48 hrs
= 500(48) = 24000 m - 24 km
area after 48 hrs
= π(24^2) = 576 km^2

growth of spill between 24 hrs and 48 hrs
= 432 km^2

But why would you subtract the 576 and 144. and plus to find the circumference you were supposed to times the 576 by pi and the 144 by pi

just multiply the answer reiny got by pi

I agree with tbetzz

To find out how many square kilometers the oil spill grew between 24 hours and 48 hours, we need to calculate the difference in area covered by the spill.

First, let's calculate the initial area of the spill at 24 hours. The formula to calculate the area of a circle is:

Area = pi * radius^2

Given that the radius grows by 500 meters every hour, we can calculate the initial radius at 24 hours:

Radius at 24 hours = initial radius + growth rate * time
= (500 m/hour) * 24 hours
= 12,000 meters

Now, let's calculate the area covered by the spill at 24 hours:

Area at 24 hours = pi * (radius at 24 hours)^2
= 3.14 * (12,000 meters)^2
≈ 452,160,000 square meters

Next, let's calculate the area covered by the spill at 48 hours. Using the same logic, we can calculate the radius at 48 hours:

Radius at 48 hours = initial radius + growth rate * time
= (500 m/hour) * 48 hours
= 24,000 meters

Then, we can calculate the area covered by the spill at 48 hours:

Area at 48 hours = pi * (radius at 48 hours)^2
= 3.14 * (24,000 meters)^2
≈ 1,809,280,000 square meters

Finally, to find the difference in area between 24 and 48 hours, we subtract the initial area from the final area:

Difference in area = Area at 48 hours - Area at 24 hours
= 1,809,280,000 square meters - 452,160,000 square meters
= 1,357,120,000 square meters

To convert this to square kilometers, we divide the difference in area by 1,000,000:

Difference in area (in square kilometers) = Difference in area / 1,000,000
= 1,357,120,000 square meters / 1,000,000
= 1,357.12 square kilometers

Therefore, between 24 hours and 48 hours, the oil spill grew by approximately 1,357.12 square kilometers.