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I think it's 50 now
A 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)

Respuesta :

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

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