Question

One hexagonal prism has dimensions that are triple the dimensions of a similar hexagonal prism. If the volume of the smaller prism is 4.75 cm 3 , what is the volume of the larger prism?

Answer 1

Answer:$128.25$

Explanation:

Given

Smaller Prism volume $=4.75 cm^3$

and it is given that the larger prism has dimensions that are triple the dimension of a similar hexagonal prism

and we know volume of prism is given by

$V=\frac{3\sqrt{3}}{2}a^2h$

where a=side of hexagon

H=height of prism

larger prism dimensions

a'=3a

h'=3h

$V_{larger}=\frac{3\sqrt{3}}{2}(3a)^2(3h)$

$V_{larger}=27V_{original}$

$V_{larger}=128.25 cm^3$