Question

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)

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

Explanation:

Answer 2

p(t)=6t

A(p)=πp^2, since p(t)=6t

A(t)=π(p(t))^2

A(t)=π(6t)^2

A(t)=36πt^2, so when t=8 and approximating π≈3.14

A(8)≈36(3.14)(8^2)

A(8)≈36(3.14)64

A(8)≈7234.56 u^2