Chapter 5: Q. 68 (page 257)

The spread of oil leaking from a tanker is in the shape of a circle. If the radius $r$ (in feet) of the spread after $t$ hours is $r (t) = 200 \sqrt{t}$ , find the area $A$ of the oil slick as a function of the time $t$ .

Short Answer

Expert verified

The Area, $A (t) = 40, 000 πt .$

Step by step solution

Step 1. Given Information

Given that $r (t) = 200 \sqrt{t} .$

Step 2. Solution

We know that the area of circle is $A (r) = {πr}^{2} .$

We have to find area $A$ as a function of $t .$

Here, $r (t) = 200 \sqrt{t} .$

So,

$A \circ r (t) = A (r (t)) A \circ r (t) = π {r (t)}^{2} A \circ r (t) = π {200 \sqrt{t}}^{2} A \circ r (t) = π {40000 t} A \circ r (t) = 40, 000 πt A (t) = 40, 000 πt .$

Step 3. Final answer

Hence, $A$ as a function of $t$ is $A (t) = 40, 000 πt .$

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The spread of oil leaking from a tanker is in the shape of a circle. If the radius $r$ (in feet) of the spread after $t$ hours is $r (t) = 200 \sqrt{t}$ , find the area $A$ of the oil slick as a function of the time $t$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

Step 3. Final answer

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The spread of oil leaking from a tanker is in the shape of a circle. If the radius r(in feet) of the spread after thours is r(t)=200t, find the area A of the oil slick as a function of the time t.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

Step 3. Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Decision Maths

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The spread of oil leaking from a tanker is in the shape of a circle. If the radius $r$ (in feet) of the spread after $t$ hours is $r (t) = 200 \sqrt{t}$ , find the area $A$ of the oil slick as a function of the time $t$ .