Question

(07.09 HC) 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 Alp) = mp Part A: Find the area of the circle of spilled paint as a function of time, or Alp(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 r in this problem. (4 points) (10 points)

Answer 1

In this problem the expression that represente the paint in terms of time is:

$p(t)=6t$

and the area is represent as:

$A(p)=\pi p^2$

Part A: So to have the area in terms of p we can replace the first equation in the secon one so wi will get:

$\begin{gathered} A(t)=\pi(6t)^2 \\ A(t)=36\pi t^2 \end{gathered}$

Part B: now we can replace the 8 minutes in the equation so we get:

$\begin{gathered} A(8)=36\cdot3.14\cdot8^2 \\ A(8)=7234.56 \end{gathered}$