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 the volume of the cube is:
A. 1/2
B. 3/(2*pi)
C. 9/(pi)
D. 3/pi
GATE 2021 · General Aptitude · Volume · medium
Answer: The ratio of the volume of the cylinder to the volume of the cube is 3/pi.
Form cylinder from sheet M: Short edges (1 cm) brought together => circumference = 6 cm, height = 1 cm. r = 6/(2*pi) = 3/pi
Volume of cylinder: V_cylinder = pi * (3/pi)^2 * 1 = pi * 9/pi^2 = 9/pi
Form cube from sheet N: Total area = 6*1 = 6 cm^2. Each face = 1 cm^2. Side a = 1 cm. V_cube = 1^3 = 1