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You have a large metal box filled with honey, where the width is 14 cm, the length is half its size, and the volume is 1176 cm. You then open the bottom of the box, where the honey drips out at 0.5 cm What is the rate that the volume is decreasing at?

You have a large metal box filled with honey, where the width is 14 cm, the length is half its size, and the volume is 1176 cm. You then open the bottom of the box, where the honey drips out at 0.5 cm What is the rate that the volume is decreasing at?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** You have a large metal box filled with honey, where the width is \(14 \, \text{cm}\), the length is half its size, and the volume is \(1176 \, \text{cm}^3\). You then open the bottom of the box, where the honey drips out at \(0.5 \, \frac{\text{cm}^3}{\text{s}}\). What is the rate that the volume is decreasing at? --- **Explanation:** This scenario describes a box where dimensions and volume are given, and the honey is leaving the box at a known rate. The goal is to find the rate of volume decrease, which is the same as the rate of honey dripping out, expressed in \(\text{cm}^3/\text{s}\). This can be used to solve related rates problems or to apply differential calculus in real-life situations.
Transcribed Image Text:**Problem Statement:** You have a large metal box filled with honey, where the width is \(14 \, \text{cm}\), the length is half its size, and the volume is \(1176 \, \text{cm}^3\). You then open the bottom of the box, where the honey drips out at \(0.5 \, \frac{\text{cm}^3}{\text{s}}\). What is the rate that the volume is decreasing at? --- **Explanation:** This scenario describes a box where dimensions and volume are given, and the honey is leaving the box at a known rate. The goal is to find the rate of volume decrease, which is the same as the rate of honey dripping out, expressed in \(\text{cm}^3/\text{s}\). This can be used to solve related rates problems or to apply differential calculus in real-life situations.
Expert Solution
Step 1

For the metal box, it is given that width is b=14 cm,

Length is half of width, l=7 cm, 

Volume is V=1176 cm3

⇒V=lbh⇒1176=7×14×h⇒h=12 cm

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