Question

a right circular cylinder of radius 3m amd height 7m is forged into a hexagonal prism of side 1m . find the height of prism​

Answer 1

$volume \: of \: cylinder = \pi \: {r}^{2} h \\ = \frac{22}{7} \times {3}^{2} \times 7 \\ = 22 \times 9 = 198$

$volume \: of \: prism = \frac{3 \sqrt{3} }{2} \times {a}^{2} \times h \\ 198 = \frac{3 \sqrt{3} }{2} \times {1}^{2} \times h \\ h = \frac{198 \times 2}{3 \sqrt{3} } \\ = \frac{132}{ \sqrt{3} } \\ = \frac{44\times \sqrt{3} \times \sqrt{3} }{ \sqrt{3} } \\ = 44 \sqrt{3}$