Question

These are numeric entry type questions.
A model of a prism is made with three identical rectangular and two identical triangular cardboard pieces of negligible thickness. If the dimensions of a rectangular piece are 8 $\sqrt{3}cm\times 8cm$, then the minimum volume of the air enclosed in the prism (in cu cm) will be_____

Answer 1

Answer: 384

Since the rectangular pieces are identical, the triangular base should be an equilateral triangle of side $8cm$ or $8\sqrt{3}cm$.
$\therefore$ Volume of the air inside the model of the prism $=Ah$
Case (i) $V=\frac{\sqrt{3}}{4}\times (8{)}^2\times 8\sqrt{3}$ $V=384cucm$
Case (ii) $V=\frac{\sqrt{3}}{4}\times (8\sqrt{3}{)}^2\times 8$ $=384\sqrt{3}cucm$