A right circular solid cylinder has radius of base $$7 cm$$ and height is $$28 cm$$. It is melted to form a cuboid such that the ratio of its side is 2 : 3 : 6. What is the total surface area (in $$cm^2$$) cuboid?

Volume of cylinder= $$\pi\times\left(r\right)^2\times h=\frac{22}{7}\times7^2\times28=4312\ cm^2\ .$$

Let say, sides of cuboid 2k,3k and 6k.

So, $$2k\times3k\times6k=4312\ .$$

or, $$k^3=\frac{4312}{36}=\frac{1078}{9}\ .$$

or, $$k=\sqrt[\ ]{\frac{1078}{9}}\ .$$

So, Total Surface Area= $$2\left(3k\times2k+2k\times6k+3k\times6k\right)=2\left(6k^2+12k^2+18k^2\right)=72k^2.$$

or, SA= $$72\left(\sqrt[\ 3]{\frac{1078}{9}}\right)^2.$$

E is correct choice.