Math Help-Grade 10- Equation of a Circle Question!

A raindrop falls into a puddle, creating a circular ripple. The radius of the ripple grows at a steady rate of 5cm/s. If the origin is used as the location where the raindrop hits the puddle, determine an equation that models the ripple exactly 6 s after the raindrop hits the puddle.

The answer is x2 + y2 = 900.

How do you do this question? In steps?

Equation for a circle:
     (x−h)² + (y−k)² = r²
where
     center is (h, k)
     r is the radius

radius r = 6 seconds × (5 cm/second) = 30 cm
center (h, k) = (0, 0)

(x−0)² + (y−0)² = 30²
x² + y² = 900

x^2 + y^2 = C^2 is the equation for a circle with radius C with the origin as the center
Now after 6 seconds the radius = 6 * 5 = 30
so x^2 + y^2 = (30)^2

You can also add that for any time the equation is x^2 + y^2 = (5 * t)^2

If r = 5, you know that x^2 + y^2 = 5^2 because of the Pythagorean theorem.
(You can make a right triangle for all points that do not intercept the x or y axes.)

6s x 5cm/s = 30 cm
x^2 + y^2 = 30^2cm^2 or
x^2 + y^2 = 900cm^2

At t=0 Circle is x^2 + y^2 =0 r=0
At t=1 Circle is x^2 + y^2 =25 r=5
At t=2 Circle is x^2 + y^2 =100 r=10
At t=3 Circle is x^2 + y^2 =225 r=15
At t=4 Circle is x^2 + y^2 =400 r=20
At t=5 Circle is x^2 + y^2 =625 r=25
At t=6 Circle is x^2 + y^2 =900 r=30

So formula is x^2+y^2= 25 (t)^2

it grows at the rate of 5cm/s
therefore after 6 seconds, radius = 5x6 = 30

since the center is the origin
euation
x^2 + y^2 = 30^2

= x^2 + y^2 = 900