Question

A metallic triangular prism has a height 15 cm and a base as a right angled triangle, with dimensions as base 3 cm & altitude 4 cm. If the prism is melted and recast into cubes of side $1cm$, then how many cubes are cast?

Answer 1

Volume of the triangular prism = $BaseArea\times Height$

A = Area of triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times 3\times 4=6c{m}^2$

Volume of prism $=6\times h$

$=6\times 15$

$=90c{m}^3$

It is melted into cubes of side 1 cm

Let n be the no. of cubes obtained

Volume of prism = $=n\times volumeofeachcube$

90 $=n\times (1cm{)}^3$

$n=90$

Hence, 90 cubes are cast from the prism.