Answer:
(D) 45 cm^3
Explanation:
The formula for the volume of a rectangular prism is given by:
V = LWH, where
- V is the volume in units cubed,
- L is the length,
- W is the width,
- and H is the height.
Since the prism's original volume is 30 cm³, we have:
Original Volume = L W H = 30 cm³
Since the length is doubled, the width is tripled, and the height is divided by four, the formula for the new volume is given by:
New Volume = (2L)(3W)(H/4)
Now we can simplify the expression:
New Volume = 2 × 3 × (L × W × H / 4)
New Volume = 6 × (L × W × H / 4)
New Volume = (6 / 4) × (L × W × H)
New Volume = (3 / 2) × (L × W × H)
- Thus, the original volume changes by a factor of 3/2.
Thus, we can find the New Volume using the formula:
New Volume = (3 / 2) × 30 cm³
New Volume = 45 cm³
Therefore, the volume of the new prism is 45 cm³, so the correct answer is D.