Question

The volume of a cylinder is $48.125c{m}^3$, which is formed by rolling a rectangular paper sheet along the length of the paper. If a cuboidal box (without any lid i.e., open at the top) is made from the same sheet of paper by cutting out the square of side 0.5 cm from each of the four corners of the paper sheet, then what is the volume of this box?

• A. $20c{m}^3$
• B. $38c{m}^3$
• C. $19c{m}^3$
• D. None of these

Answer 1

The correct option is A

$20c{m}^3$

$l=2\pi r\Rightarrow r=\frac{l}{2\pi }$


where r is the base radius of cylinder and l is the length of paper and h = b, where h is the height of cylinder and b is the breadth of the paper.
$\begin{array}{ccc}\therefore & \text{Volume of cylinder}=\pi r^{2}h=\pi \times {\left(\frac{l}{2\pi }\right)}^2\times b& \\ \Rightarrow & \frac{\pi \times l^{2}b}{4{\pi }^2}=48.125=\frac{385}{8}& \\ \Rightarrow & l^{2}b=11\times 11\times 5& \\ \Rightarrow & l=11\text{and}b=5& (\because l>b)\\ \therefore & \text{Volume of the box}=l\times b\times 4& \\ & =10\times 4\times 0.5=20c{m}^3& \end{array}$