Question

On March 24, 1989, the Exxon Valdez oil tanker ran aground and leaked millions of gallons of oil into Prince William Sound. The spill covered approximately 11,000 square miles of ocean. The oil spread out in a circular pattern and the radius increased by 0.10 mph. Use π = 3.14. At this rate, how many hours did it take for oil to cover the area?

Answer 1

Answer: B

592 hours

Explanation:

Answer 2

592 hours

Explanation:

Given

`Area = 11000m^2`

`Radius = 0.10m/h`

Required

Determine the time taken to cover the area

Since, the oil formed a circular pattern; the question will be answered using area of a circle

`Area = \pi r^2`

Let t represent the time take to cover 11000m²;

The relationship between these parameters is:

`11000 = \pi * (0.10t)^2`

Substitute 3.14 for π

`11000 = 3.14 * (0.10t)^2`

Divide both sides by 3.14

`(11000)/(3.14) = (3.14 * (0.10t)^2)/(3.14)`

`(11000)/(3.14) =(0.10t)^2`

`3503.18471338 = (0.10t)^2`

Take square root of both sides

`√(3503.18471338) = √((0.10t)^2)`

`√(3503.18471338) = 0.10t`

`59.1877074516 = 0.10t`

Divide both sides by 0.10

`(59.1877074516)/(0.10) = (0.10t)/(0.10)`

`(59.1877074516)/(0.10) = t`

`591.877074516 = t`

`t = 591.877074516`

`t = 592\ hours` (Approximated)

Hence, it'll take approximately 592 hours to cover the given area