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 $\sqrt{3} cm \times 8 cm$, then the minimum volume of the air enclosed in the prism (in cu cm) will be_____

Answer 1

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