Question

A triangular prism has a volume of 5 m3. If each dimension of the prism is tripled, what is the new volume of the prism?
Answer

135 m3

45 m3

15 m3

405 m3

Answer 1

and i chose 15

Answer 2

well since Volume of a triangular prism is V=5m^3
and the formula is:
\[\LARGE V=\frac12 bhl\]
now , if EACH dimension of the prism is tripled which mean 3times...
we have
\[\LARGE V=\frac12 \cdot 3\cdot b\cdot 3\cdot h\cdot 3\cdot l\]
so in total there is 81 times Volume of the Prism we had at principal...
which means
if
\[\LARGE V=\frac12 bhl\]
\[\LARGE V=5 m^3\]
and now
\[\LARGE V=81\cdot \frac12 bhl\]
we also raise 5m^3 by
\[\LARGE V=81\cdot 5 m^3\]
and when we multiply it out, we see that the new Volume of this prism is:
V=405 m^3