GATE 2017 ME (ME1) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A right circular cone of base radius 5 cm and height 12 cm is rolled on the ground while its apex P stays fixed, until the marked base point Q touches the ground again. Through what angle in radians about P does it travel?

Diagram for GATE 2017 ME (ME1) question 3

$5\pi/12$
$5\pi/24$
$24\pi/5$
$10\pi/13$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $10\pi/13$

Explanation

The slant height is $s=\sqrt{5^2+12^2}=13$ cm. Unrolling the lateral cone surface gives a sector of radius 13 cm and arc length equal to the base circumference $2\pi(5)=10\pi$ cm. The sector angle is arc length divided by radius, $\theta=10\pi/13$ radians. Rolling once until Q returns to the ground sweeps this angle about the fixed apex, giving D.

More Quantitative Aptitude: Algebra, Geometry and Mensuration questions

GATE 2017 ME (ME1) Q8 – Let S 1 consist of (x,y) satisfying x-1 2, y+2 3. Let S 2 satisfy x-y-2, y1, x3. Find the…
GATE 2025 CS (CS1) Q7 – In the diagram, the lines QR and ST are parallel to each other. The shortest distance…
GATE 2025 CS (CS2) Q3 – If Pex = Qe-x for all real values of x, which one of the following statements is true?
GATE 2025 CS (CS2) Q9 – In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L…
GATE 2024 CS (CS1) Q2 – If two distinct non-zero real variables x and y are such that (x+y) is proportional to…
GATE 2024 CS (CS1) Q5 – For positive non-zero real variables p and q, if (p2+q2)= p+ q+2 3, then the value of…

All Quantitative Aptitude: Algebra, Geometry and Mensuration questions →