First, we determine the volume of the prism by multiplying the area of the base by the height.
Volume = (base area) x (height)
Volume = (3 m²)(4 m) = 12 m³
By "dilated" we mean to say that the dimensions of the prisms are enlarged by that factor. The cube of this dilation ratio is equal to the ratio of the volumes. If we let x be the volume of the new prism,
x/12 m³ = (3/2)³
The value of x from the equation is 40.5 m³.
Thus, the volume of the dilated prism is approximately 40.5 m³.
