A ball is thrown into a lake, creating a circular ripple that travels outward at a speed of 5 cm per second. Express the area, A = , of the circle in terms of the time, t , (in seconds) that have passed since the ball hits the lake.1 point𝐴=25𝜋𝑡A=25πt𝐴=𝜋𝑡2A=πt 2 𝐴=5𝜋𝑡2A=5πt 2 𝐴=25𝜋𝑡2A=25πt 2 𝐴=10𝜋𝑡A=10πt
Question
A ball is thrown into a lake, creating a circular ripple that travels outward at a speed of 5 cm per second. Express the area, A = , of the circle in terms of the time, t , (in seconds) that have passed since the ball hits the lake.1 point𝐴=25𝜋𝑡A=25πt𝐴=𝜋𝑡2A=πt 2 𝐴=5𝜋𝑡2A=5πt 2 𝐴=25𝜋𝑡2A=25πt 2 𝐴=10𝜋𝑡A=10πt
Solution
The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the radius of the circle is the distance the ripple has traveled, which is the speed of the ripple times the time that has passed. So, r = 5t. Substituting this into the formula for the area gives A = π(5t)² = 25πt². So, the area of the circle in terms of the time that has passed since the ball hit the lake is A = 25πt².
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