Answer:
The value of the new volume 'x' would be equal to 40.5 cm³.
Step-by-step explanation:
Given
We can determine the volume of the original prism by multiplying the area of the base by the height,
volume = (3 cm²)(4 cm) = 12 cm³
Dilation by a factor of 3/2 means that the dimensions of the new prism is 3/2 times that of the original object.
let 'x' be the volume of the new solid,
[tex]\frac{x}{12}=\left(\frac{3}{2}\right)^3[/tex]
[tex]\frac{x}{12}=\frac{27}{8}[/tex]
Multiply both sides by 12
[tex]\frac{12x}{12}=\frac{27\cdot \:12}{8}[/tex]
[tex]x=\frac{81}{2}[/tex]
[tex]x=40.5[/tex] cm³
Therefore, the value of the new volume 'x' would be equal to 40.5 cm³.
