Question

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function r(t) = 3t, where t represents time in minutes and r represents how far the paint is spreading.

The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.

Part A: Find the area of the circle of spilled paint as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled paint after 10 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

r(t) = 3t ; where t represents the time in minutes and r represents how far the paint is spreading.
A(r) = πr²

Part A:
A[r(t)] = π (3t)² = 3.14 * 9t² = 28.26t²

Part B:
r(10) = 3(10) = 30
A(r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit

Hope This Helped! :3