Chapter 2.8, Problem 27E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of

To determine

**To find:**

How fast is the water level rising when water is 30 cm deep?

Explanation

**1. Concept:**

We can plot the figure from the given situation

Here we have to find the rate at which the height of the water is rising in the trough.

Then we can consider the trapezoid and divide it into rectangles and triangles to write the formula of volume of trapezoid. After differentiating with respect to time, we can find the required rate.

**2. Formula:**

i. Volume of isosceles trapezoid = Area of trapezoid * length

ii. Power rule of differentiation:

iii. Chain rule of differentiation:

**3. Given:**

i.

ii. Length of trough, l = 10m

**4. Calculations:**

Let

Volume of isosceles trapezoid is

If we draw the trapezoid and divide it into rectangles with base 0.3

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