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A right-angled cone (with base radius 5 cm and height 12 cm), as shown in fte figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.
By what angle (in radians) about P does the cone travel?
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5π 12 -
5π 24 -
24π 5 -
10π 13
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Correct Option: D
Base radius = 5cm, Height = 12 cm. So Slant Height = 13cm.
If, we open it now then it appears as an arc with its radius = Slant Height of the cone = 13 cm.
Length of the arc = Circumfernce of the cone = 2×pie×5 = 10 pie cm
Now, when, length of arc is 2×p×13, angle subtended is 2pie.
So, angle subtended when length of arc is 10pie
= 2pie/26pie × 10pie = 10pie/13.
