A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r (t) = 4t, where t represents time in minutes and r represents how far the milk is spreading.

The spilled milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A (r) = πr2.

Question

Butternut

Mathematics

11 May, 06:01

A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r (t) = 4t, where t represents time in minutes and r represents how far the milk is spreading.

The spilled milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A (r) = πr2.

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Answers (1)

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Grant Gill · Answer 1

Part A: Find the area of the circle of spilled milk as a function of time, or A[r (t) ].

A (r (t)) = A (4t) = π (4t) ^2 = 16πt^2

A[r (t) ] = 16πt^2

Part B: How large is the area of spilled milk after 4 minutes? You may use 3.14 to approximate π in this problem.

After 4 minutes, A = 16 (3.14) (4) ^2 = 803.84 cubic meters.