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Navigating the Cone (Posted on 2024-11-05)

A right circular cone of base radius 17cm and slant height 51cm is given. P is a point on the circumference of the base. Find the length of the shortest path from P around the cone and back to P.

No Solution Yet Submitted by Danish Ahmed Khan

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The circumference of the base is 2*pi*17 =~ 106.8 cm.

Cut along a slant height and laid out flat, the bounding arc is part of a circle of circumfernece of about 320.4. The arc is exactly 1/3 the entire circumference of its laid-out circle, or 120°.

The length of the chord is 2*51*sin(60°) and that is the length of the shortest path. It's about 88.3346 cm.

Posted by Charlie on 2024-11-05 08:41:33

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