AP EAMCET · Maths · Application of Derivatives
The height of the cone of maximum volume inscribed in a sphere of radius \(R\) is
- A \(\frac{R}{3}\)
- B \(\frac{2 R}{3}\)
- C \(\frac{4 R}{3}\)
- D \(\frac{4 R}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(C) \(\frac{4 R}{3}\)
Step-by-step Solution
Detailed explanation
Let the height of the cone \(=h\) and the radius of the cone \(=r\) Given, radius of the sphere \(=R\) Now, In \(\triangle O P B\) \(\Rightarrow \quad R^2=r^2+(h-R)^2\) \(\Rightarrow \quad r^2=R^2-(h-R)^2\) \(=(R+h-R)(R-h+R)\) \(\Rightarrow \quad r^2=h(2 R-h)\) The volume of the…
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