
A rightangled 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?

5π 12 
5π 24 
24π 5 
10π 13
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 × π × 5 = 10 π cm
Now, when, length of arc is 2×p×13, angle subtended is 2π.
So, angle subtended when length of arc is 10π
= 2π/26π × 10π = 10π/13.
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