Three identical cones each with base radius 3 cm are placed on their bases so that each is touching the other two. There will be one and <strong>ONLY</strong> circle that would pass through each of the vertices of the cones. What is the area of the circle?
- A. 3\pi square cm
- B. 6\pi square cm
- C. 9\pi square cm
- D. 12\pi square cm ✓
Correct Answer: D. 12\pi square cm
Explanation
The vertices of the identical cones form an equilateral triangle with side length 3+3=6 cm (same as the distance between the centers of their bases). The circumradius of this triangle is R = \frac{6}{\sqrt{3}} = 2\sqrt{3}. The area of the circle is \pi R^2 = \pi(2\sqrt{3})^2 = 12\pi cm^2.
Related questions on Mensuration
- A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
- A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
- A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
- A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
- Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...