Question

A rectangular tin sheet is 22 m long and 8 m broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder (in m${}^3$) is

• A. 385
• B. 204
• C. 280 $\pi$
• D. 308

Answer 1

Answer: (D)

308

Since cylinder is rolled along the length of the sheet

$\therefore$ Area of sheet $=$ curved surface area of cylinder

$⟹l\times b=2\pi rb$ $[\because$ Height of the cylinder $=$ breadth of the rectangular sheet $]$

$⟹r=\frac{22}{2\pi }=\frac{11}{\pi }\text{m}$

Volume of cylinder $=\pi r^{2}b$

$=\pi \times \frac{11}{\pi }\times \frac{11}{\pi }\times 8=308{\text{m}}^3$