Question

A rectangular paper $11$ cm by $8$ cm can be exactly wrapped to cover the curved surface of a cylinder of height $8$ cm. The volume of the cylinder is

• A. $66$ $c{m}^3$
• B. $77$ $c{m}^3$
• C. $88$ $c{m}^3$
• D. $121$ $c{m}^3$

Answer 1

The correct option is B $77$ $c{m}^3$

Area of paper$=$CSA of cylinder

$\Rightarrow l\times b=2\pi rh$

$\Rightarrow 11\times 8=2\times \frac{22}{7}\times r\times 8$

$\Rightarrow r=\frac{11\times 8\times 7}{44\times 8}=\frac{7}{4}cm$

$\therefore$Volume of cylinder$=\pi r^{2}h=\frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 8$

$=77c{m}^3$