Question:medium
Ram places three identical cones of radius on a table in such a way that each cone base touches the other two, also the altitude of the cone is perpendicular to the table. The radius of the circle drawn through the cone vertices would be?
Ram places three identical cones of radius on a table in such a way that each cone base touches the other two, also the altitude of the cone is perpendicular to the table. The radius of the circle drawn through the cone vertices would be?
Updated On: Aug 18, 2026
- Smaller than r
- Equal to r
- Larger than r
- Cannot be determined
Show Solution
The Correct Option is C
Solution and Explanation
Step 1: The three cone centers form an equilateral triangle of side \( 2r \), since each pair of bases touches.
Step 2: By the law of sines, \( 2R = \dfrac{2r}{\sin 60 \degree} \).
Step 3: This gives \( R = \dfrac{2r}{\sqrt{3}} \approx 1.155r \), which is larger than \( r \).
\[ \boxed{R \gt r} \]
Step 2: By the law of sines, \( 2R = \dfrac{2r}{\sin 60 \degree} \).
Step 3: This gives \( R = \dfrac{2r}{\sqrt{3}} \approx 1.155r \), which is larger than \( r \).
\[ \boxed{R \gt r} \]
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