A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents time in minutes and p 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(p) = πp2.

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

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)


  1. [MA]:
    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 units.
    Writer’s note: Hope this helps!


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