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.

Part B: How large is the area of spilled paint after 10 minutes? You may use 3.14 to approximate π in this problem.

Question

Mathematics

Yareli Park

29 May, 23:02

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.

Part B: How large is the area of spilled paint after 10 minutes? You may use 3.14 to approximate π in this problem.

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Answers (1)

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Phoenix · Answer 1

R (t) = 3t; where t represents the time in minutes and r represents how far the paint is spreading.

A (r) = πr²

Part A:

A[r (t) ] = π (3t) ² = 3.14 * 9t² = 28.26t²

Part B:

r (10) = 3 (10) = 30

A (r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit