GATE (GA) Textile 2021 Question Paper Solution | GATE/2021/GA/06

Question 06 (Quantitative Aptitude)
Q.6 We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is __________.
(A)\frac{\pi}{2}
(B)\frac{3}{\pi}
(C)\frac{9}{\pi}
(D)3\pi
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Dimension of ractangular sheet-

Let,length(a)=6 cm width(b)=1 cm

Volume of cube=1^3

Volume of cube=1

Now ,cylinder dimension ,peripheral(P)=6 cm length(h)=1cm

Volume of cylinder=\pi \times r^2 \times h

P=2 \times \pi \times r where r is the radius of the cylinder

6=2 \times \pi \times r

r=\frac{6}{2 \times \pi} ,

r=\frac{3}{\pi}

Volume of cylinder=\pi \times r^2 \times h

Volume of cylinder=\pi \times \frac{3}{\pi}^2 \times 1

Volume of cylinder=\frac{9}{\pi}

Ratio of volume of cylinder and volume of cube=\frac{9}{\pi} (Ans)

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