I think it's 50 nowA barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.The spilled sauce 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 sauce as a function of time, or A[r(t)]. Show your work. (6 points)Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Here barrel of tomato sauce has spilled on a tile floor. The function [tex]r(t)=2t[/tex] represents how the sauce is flowing, where, 't' represents time in minutes, and 'r' represents how far the sauce is spreading. The spilled sauce is creating a circular pattern on the tile and the area of pattern is expressed as [tex]A(r)=\pi\times r^2[/tex]A. Now we have to find the area of circle of spilled sauce as a function of time: [tex]A(r(t))[/tex]. Now, we know that [tex]A=\pi r^2[/tex]and [tex]r(t)=2t[/tex]plugging the value of 'r' as function of time in the area of the pattern, we get: [tex]A(r(t))=\pi \times (2t)^2=\pi \times 4t^2=4\pi t^2[/tex]So the area of the circular pattern as a function of time is given as: [tex]A=4 \pi t^2[/tex]B. We have to find how large is the area of spilled sauce after 5 minutes. plugging the value of 't' in the equation of the area as a function of time, [tex]t=5[/tex]we get: [tex]A(t)=4 \times \pi \times (5)^2=4 \pi \times 25=100 \pi=314[/tex](we have taken [tex]\pi=3.14[/tex])Therefore, [tex]A=314[/tex] square units