TS EAMCET · Maths · Application of Derivatives
The semi vertical angle of a right circular cone is \(30^{\circ}\). If the height of the cone is \(6.125 \mathrm{~cm}\), then the approximate value of the volume of the cone (in cubic \(\mathrm{cm}\) ) is
- A \((23.5) \pi\)
- B \((76.5) \pi\)
- C \(48 \pi\)
- D \((25.5) \pi\)
Answer & Solution
Correct Answer
(D) \((25.5) \pi\)
Step-by-step Solution
Detailed explanation
\begin{array}{rlrl} h =6.125 {~cm}, l=?, R=?, \theta=30^{\circ} \\ \therefore \quad \tan 30^{\circ} =R / h \\ \Rightarrow \quad R =h \tan 30^{\circ} \Rightarrow R=6.125 / \sqrt{3} \\ \therefore \quad V_{\text {cone }} =\frac{1}{3} \pi R^2 h=\frac{\pi}{3}\left(\frac{6.125 \times…
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