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.

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

Answer 1

part A: A[r(t)]=pi(3t)squared

*distribute the power of 2 to the 3 and t*

3.14 x 9t squared

*multiply 3.14 and 9*

ANSWER: 28.26t squared

part B: (10)=3(10)=30

A(r)=3.14 x 30 squared

3.14 x 900

ANSWER: 2826 square unit

Explanation:

i did the test

Answer 2

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