Question

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?

Answer 1

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 $m^3$

Answer 2

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!