A rock is thrown in a pond, and creates circular ripples whose radius increases at a rate of 0.2 meter per second. What will be the value of ๐ด๐ฯAโ , where ๐ดA is the area (in square meter) of the circle after 25 seconds?Hint: The area of a circle = ๐๐2ฯr 2 , where ๐r is the radius of the circle.
Question
A rock is thrown in a pond, and creates circular ripples whose radius increases at a rate of 0.2 meter per second. What will be the value of ๐ด๐ฯAโ , where ๐ดA is the area (in square meter) of the circle after 25 seconds?Hint: The area of a circle = ๐๐2ฯr 2 , where ๐r is the radius of the circle.
Solution
The radius of the circular ripples increases at a rate of 0.2 meter per second. So, after 25 seconds, the radius of the circle would be 0.2 * 25 = 5 meters.
The formula for the area of a circle is ๐๐^2. Substituting r = 5 meters into the formula gives us the area A = ๐ * (5^2) = 25๐ square meters.
So, the value of ๐ด๐ (which is the area of the circle divided by ๐) would be 25๐/๐ = 25.
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