Question

Please help I don't understand.

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.

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

Answer 1

Part A

`A(p) =2p \pi \\ p(t) = 6t \\ A(p(t)) = 2 * 6t * \pi = 12t\pi`

Part B

`A(p(8)) = 12 * 8 * \pi = 301.44 \: u {}^(2) \\`