Respuesta :
Volume of Original Prism = base area * Height = 3 * 4 = 12
After dilation factor = 12 * 3/2 = 6 * 3 = 18
In short, Your Answer would be 18 m³
Hope this helps!
After dilation factor = 12 * 3/2 = 6 * 3 = 18
In short, Your Answer would be 18 m³
Hope this helps!
Answer:
Scale factor(k)defined as the ratio of image to the pre-image i,e
[tex]k = \frac{\text{Image}}{\text{Pre-image}}[/tex]
Volume of a prism is given by:
[tex]V = A \cdot h[/tex]
where
V is the volume of the prism
A is the base Area
h is the height.
As per the statement:
A prism with a base area of 3 m² and a height of 4 m
⇒Base area(A) = 3 m² and height(h) = 4 m
Then by definition of volume of prism
Volume of the original prism = [tex]3 \cdot 4 = 12 m^3[/tex]
Since, the prism is dilated by a factor of 3/2
⇒[tex]k = \frac{3}{2}[/tex]
then by definition of scale factor:
[tex]k= \frac{\text{Dilated volume of prism}}{\text{Original prism}}[/tex]
Substitute the given values we have;
[tex]\frac{3}{2} = \frac{\text{Dilated Volume of prism}}{12}[/tex]
Multiply both sides by 12 we have;
[tex]\text{Volume of dilated prism} = 12 \cdot \frac{3}{2} = 6 \cdot 3 = 18[/tex] cubic meter
Therefore, the volume of dilated prism is, 18 [tex]m^3[/tex]
