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

@jim_thompson5910

Answer 2

Part A: You will plug in 3t to A(r) = pir^2
When you plug in the 3t you get:
A[r(t)]= pi(3t)^2
=pi * (3t)^2
=pi * (3t * 3t)
=9pit^2

Answer 3

Part B: 10= t, because you need area after 10 minutes:
9π(10^2)=900π = 900 x 3.14=2826 sq units.

Answer 4

Thank you.

Answer 5

you're welcome :)