What is the radius of the sphere?
Consider the following for the next three (03) items that follow:<br><br>A conical vessel of radius 12 cm and height 16 cm is filled with water. A sphere is lowered into water and its size is such that it touches the sides of the vessel and it is just immersed.
- A. 5 cm
- B. 6 cm ✓
- C. 6.5 cm
- D. 7 cm
Correct Answer: B. 6 cm
Explanation
The cross-section is an isosceles triangle with base 24 and height 16. The slant height l = \sqrt{12^2+16^2} = 20. The radius of the inscribed sphere R equals the inradius of this triangle. R = \frac{\text{Area}}{\text{Semi-perimeter}} = \frac{\frac{1}{2} \times 24 \times 16}{\frac{1}{2}(20+20+24)} = \frac{192}{32} = 6\text{ cm}.
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