Question

Two cubes each of volume 64 $c{m}^3$ are joined to form a cuboid. Find the L.S.A and T.S.A of the resulting solid.

Answer 1

Volume of each cube $=64c{m}^3=lengh{t}^3$

Then, length$=$ ${}^3\sqrt{64}=4cm$

Then when the two cubes are merged, the length increases whereas the base and height remains intact. Hence the dimension becomes : $8\times 4\times 4$

So the Lateral Surface area of the cuboid $=2h(l+b)=2\times 4\left(12\right)=96c{m}^2$

Total surface area of the cuboid $=2(lb+bh+lh)=2(32+16+32)=160c{m}^2$