Question

Two equal rectangular sheets of dimensions $155	ext{ cm} 	imes 45	ext{ cm}$ as shown in the figure are folded to make hollow right circular cylinders in such a way that there is exactly 1 cm overlap when sticking the ends of the sheet. Sheet 1 is folded to form a cylinder of height 45 cm while sheet 2 is folded to get a cylinder of height 155 cm. Find the difference in the radii of the two cylinders and hence find the ratio of their volumes.

Accepted Answer

For Sheet 1: circumference = $155 - 1 = 154	ext{ cm} \implies 2\pi r_1 = 154 \implies r_1 = 24.5	ext{ cm}$, $h_1 = 45	ext{ cm}$. For Sheet 2: circumference = $45 - 1 = 44	ext{ cm} \implies 2\pi r_2 = 44 \implies r_2 = 7	ext{ cm}$, $h_2 = 155	ext{ cm}$. Difference in radii = $24.5 - 7 = 17.5	ext{ cm}$. Ratio of volumes = $\frac{\pi r_1^2 h_1}{\pi r_2^2 h_2} = \frac{24.5^2 	imes 45}{7^2 	imes 155} = \frac{600.25 	imes 45}{49 	imes 155} = \frac{12.25 	imes 45}{155} = \frac{551.25}{155} \approx 3.556$.

Folding sheets into cylinders

Explanation

Practise this under board exam conditions