GATE (GA) Textile 2017 Question Paper Solution | GATE/2017/GA/58

Question 58 (General Aptitude)

A right-angled cone (with base radius 5 cm and height 12 cm) as shown in the 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 radius) about P does the cone travel ?

(A)	$\frac{5\pi}{12}$
(B)	$\frac{5\pi}{24}$
(C)	$\frac{24\pi}{5}$
(D)	$\frac{10\pi}{13}$

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Given in the figure-
radius(r)=5cm
height(h)=12cm
Inclined height(slant height,l)= $\sqrt(r^2+h^2)$
l= $\sqrt(5^2+12^2)$
l= $\sqrt(169)$
l=13 cm

Here, As cone is rolling over circumference 360 deg.
Let the cone angle= $\theta$
So,
$2\pi\times r=l\times \theta$
$2\pi\times5=13\times \theta$
$\theta=\frac{10\pi}{13}$ (Ans)

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