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Chapter 3: Q. 57 (page 300)

Riley is holding an ice cream cone on a hot summer day. As usual, the cone has a small hole at the bottom, and ice cream is melting and dripping through the hole at a rate of half a cubic inch per minute. The cone has a radius of 2 inches and a height of 5 inches. How fast is the height of the ice cream changing when the height of the ice cream in the cone is 3 inches?

Short Answer

Expert verified

The rate of change is-2572蟺in

Step by step solution

01

Step 1. Given information

Given the cone has a radius of 2inches and a height of 5inches

02

Calculate volume in terms of height 

Calculating, we get

V=13蟺r2hV=13蟺25h2hV=475蟺h3

03

Differentiating the function

Differentiating, we get

dVdt=475蟺3h2脳dhdt-12=475蟺3(3)2脳dhdtdhdt=-2572蟺in

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Most popular questions from this chapter

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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