Question Bank - General Aptitude

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We have 2 rectangular sheets of paper. M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to from an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal patches and assembled to from the largest closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that cube is ______

A.
\(\frac{3}{\pi }\)
B.
\(\frac{9}{\pi }\)
C.
\(\frac{\pi }{2}\)
D.
3?

Solution:

Given:Two rectangular sheets M and N have the dimension 6 cm × 1 cm each, in which cylinder will be formed by bringing the short edges of the sheet together. Given that ends of the cylinder are closed.Concept:Volume of cylinder = ? × r2 × hThe volume of the cube = a3Calculation:Let be assume the side of the cube is a,? The area of the sheet N = 6 × a2? 6 × 1 = 6 × a2? a = 1? Volume of the cube = a3 = 13 = 1? The circumference = 6? 2 × ? × r = 6, r = 3/? and height of the cylinder = 1 cm? Volume of the cylinder = ? × (3/?)2 × 1 = 9/? ? The required ratio = 9/? : 1? The required result will be 9/? .

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