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 number of seconds, t, that have passed since the ball hits the lake. A = 25t A = 2576 A = Ar? A = 5t? None of the above

Question

Valerie Stevens

Mathematics

25 June, 01:28

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 number of seconds, t, that have passed since the ball hits the lake. A = 25t A = 2576 A = Ar? A = 5t? None of the above

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Zane · Answer 1

The area of the circular ripple after t second is

A = 25π t²

where A is in cm².

Step-by-step explanation:

Given that,

Circular ripple that travels outward at a speed of 5 cm per second.

It means that, the radius of the circular ripple increases at a seed 5 cm / s.

Therefore the radius of the circular ripple after t seconds is

r (t) = 5t

where r (t) is in cm.

We know,

The area of a circular object is = π r²

The area of the circular ripple after t second is

A = π (5t) ²

=25πt²

where A is in cm².