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Chapter 3: Q. 30 (page 288)

Use optimization techniques to answer the questions in Exercises 25鈥�30.
Find the volume of the largest cylinder that fits inside a sphere of radius 10.

Short Answer

Expert verified

The volume of the largest cylinder is V=4000蟺33.

Step by step solution

01

Step 1. Given Information.

Radius of circle is 10.

02

Step 2. Form an equation.

From the given information,

r2=R2-(h2)2V=蟺谤2h=蟺(R2-(h2)2)h

03

Step 3. Differentiate with respect to h.

On differentiating,

dVdh=蟺(hR2-h24)蟺(hR2-h24)=0

04

Step 4. Find the maximum volume.

The second derivative of the volume with respect to h is negative is h>0such that the volume is maximal at h=h0.

V=4蟺搁333=4蟺(10)333V=4000蟺33

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Most popular questions from this chapter

Explain the difference between two antiderivatives of the function.

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