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Concept explainers
21. Inscribing a Cylinder in a Cone Inscribe a right circular cylinder of height h and radius r in a cone of fixed radius R and fixed height H. see the illustration. Express the volume V of the cylinder as a function of r.
[Hint: . Note the similar triangles.]
![Check Mark](/static/check-mark.png)
To find: To express the Volume of the cylinder as a function of .
Answer to Problem 21AYU
Solution:
Explanation of Solution
Given:
A right circular cylinder of height and radius is inscribed in a sphere of fixed radius and fixed height .
Calculation:
To express the Volume of the cylinder as a function of :
Volume of a cylinder .
From the figure, based on the properties of similar triangles, the ratio of sides can be written as
Therefore,
Hence, the volume of the cylinder is .
Chapter 2 Solutions
Precalculus
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