A prism with a base area of 3 m² and a height of 4 m is dilated by a factor of 3/2 . What is the volume of the dilated prism?
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!
Answer:
Scale factor(k)defined as the ratio of image to the pre-image i,e
\(k = \frac{\text{Image}}{\text{Pre-image}}\)
Volume of a prism is given by:
\(V = A \cdot h\)
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 = \(3 \cdot 4 = 12 m^3\)
Since, the prism is dilated by a factor of 3/2
⇒\(k = \frac{3}{2}\)
then by definition of scale factor:
\(k= \frac{\text{Dilated volume of prism}}{\text{Original prism}}\)
Substitute the given values we have;
\(\frac{3}{2} = \frac{\text{Dilated Volume of prism}}{12}\)
Multiply both sides by 12 we have;
\(\text{Volume of dilated prism} = 12 \cdot \frac{3}{2} = 6 \cdot 3 = 18\) cubic meter
Therefore, the volume of dilated prism is, 18 \(m^3\)