Q.6 We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 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) π/2
• (B) 3/π
• (C) 9/π
• (D) 3π

Two 6 cm × 1 cm sheets form a cylinder and a cube, with volumes compared for the correct ratio.

Cylinder Volume Calculation

Sheet M rolls short 1 cm edges together, making 6 cm the circumference and 1 cm the height.

Circumference: 2πr = 6, so r = 3/π cm.

Volume: Vc = πr²h = π(3/π)²(1) = 9/π cm³, despite ends closed since paper forms lateral surface.

Cube Volume Calculation

Sheet N cuts into equal squares for largest closed cube.

Total area = 6 cm² fits six 1 cm × 1 cm faces exactly, side a = 1 cm.

Volume: Vb = a³ = 1 cm³.

Ratio and Correct Answer

Ratio Vc / Vb = 9/π. Correct option (C).

Options Analysis

• (A) π/2: Reverse, smaller value mismatches 9/π ≈ 2.86
• (B) 3/π: Matches if height misinterpreted as circumference — incorrect rolling
• (C) 9/π: Matches exact calculation
• (D) 3π: Swapped dimensions, larger incorrect value

Comparison Table