Question

Type the correct answer in the box.

Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of the circle measured in inches is modeled by the function r(s) = 3*sqrt(s), where s in time in seconds.

The area of the spill when s = 5 seconds is ___ π square inches.
Note: 3*sqrt(s) is not ∛s

Answer 1

The area of the oil spill when s = 5 seconds is approximately 140 π square inches, obtained by finding the radius with the given function and then calculating the area using the formula A = πr².

Step-by-step explanation:

The area of the oil spill when s = 5 seconds can be found by first calculating the radius of the oil spill using the given function r(s) = 3*sqrt(s) and then using the formula for the area of a circle, A = πr².

First, calculate the radius:

r(5) = 3*sqrt(5) = 3*2.236 = 6.708 inches (rounded to three decimal places)

Now, use the found radius to calculate the area:

A = πr² = π*(6.708²) = π*44.997664 ≈ 141.372 π square inches.

Since the area is typically given to two significant figures, as per the example provided, we round the calculated area to:

A = 140 π square inches.

Answer 2

The area of the oil spill when s = 5 seconds is approximately 44.7 π square inches, calculated by first finding the radius with the given function, then using the area of a circle formula.

Step-by-step explanation:

The area of the oil spill when s = 5 seconds is calculated using the formula for the area of a circle, A = πr², where r is the radius of the oil spill.

Given the function r(s) = 3*sqrt(s), first, we need to calculate the radius at s = 5 seconds, which is r(5) = 3 * sqrt(5). Afterwards, we find the area by squaring the radius and multiplying by π:

r(5) = 3 * sqrt(5)

= 3 * 2.236

= 6.708 inches (approximately)

A = πr²

= π * (6.708 inches)²

= 44.715 π square inches (approximately)

When working with significant figures, as the radius was calculated to three significant figures, the area can also be represented with three significant figures: A = 44.7 π square inches (approximately).