Answered: Find the dimensions of a cylinder that…

Math

Calculus

Find the dimensions of a cylinder that can fit into a hemisphere of radius 10 inches.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section1.3: Modeling With Linear Equations

Problem 9ECP: A cylindrical container has a volume of 84 cubic inches and a radius of 3 inches. Find the height of...

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Question

Find the dimensions of a cylinder that can fit into a hemisphere of radius 10 inches.

Expert Solution

Step 1

Let there is cylinder with radius r and height h that be fit in a hemisphere of radius 10 inches. So,

$\begin{array}{rcl} V o l u m e o f c y l i n d e r & = & V o l u m e o f h e m i s p h e r \\ {πr}^{2} h & = & \frac{2}{3} π {(10)}^{3} \\ h & = & \frac{2000}{3 r^{2}} . . . (1) \end{array}$

Now, the total surface of cylinder is given by,

$\begin{array}{rcl} S & = & 2 πr (r + h) \\ = & 2 πr (r + \frac{2000}{3 r^{2}}) \\ = & 2 π (r^{2} + \frac{2000}{3 r}) \end{array}$

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