Question

A hollow cylinder having volume $48.125$ $c{m}^3$ is cut along the height to form a cuboidal box (without any lid) by cutting out the square of side $0.5cm$ from each of the four corners of the paper, then find the volume of the box.

• A. $20$ $c{m}^3$
• B. $38$ $c{m}^3$
• C. $19$ $c{m}^3$
• D. $24$ $c{m}^3$

Answer 1

The correct option is A $20$ $c{m}^3$

Let length of box be $l^{\prime }$ and width be ${}^{\prime }{b}^{\prime }$. Now, the circumference of base of cylinder is equal to length of box.

$\therefore 2\pi r=l\Rightarrow r=\frac{l}{2\pi },Now\pi r^{2}h=\pi \times \frac{l^2}{4{\pi }^2}\times b=\frac{{bl}^2}{4\pi }$

$\Rightarrow \frac{{bl}^2}{4\pi }=48.125\Rightarrow l^{2}b=192.5\pi \Rightarrow b=\frac{192.5\pi }{l^2}$

Length of box = $(l-1)$, width = b -1, height = 0.5

Volume = $(l-1)(b-1)\times 0.5=0.5(l-1)(\frac{\mathrm{192.5.}\pi }{l^2}-1)=0.5(\frac{192.5\pi }{l}-l-\frac{192.5\pi }{l^2}+1)$

Hence, it is not possible to solve this question.