Question

A rectangular box has a volume of 15 cubic feet. The length, width, and height of the box are each doubled.



What is the new volume of the rectangular box?

Answer options with 4 options
A.
30 cubic feet

B.
60 cubic feet

C.
90 cubic feet

D.
120 cubic feet

Answer 1

To find the new volume of the rectangular box when its dimensions are each doubled, we can follow these steps:

1. **Original Volume**: The original volume of the box is given as 15 cubic feet.

2. **Doubling Dimensions**:
- If the original dimensions of the box are length \( l \), width \( w \), and height \( h \), the volume \( V \) is given by:
\[
V = l \times w \times h
\]
When each dimension is doubled, the new dimensions become \( 2l \), \( 2w \), and \( 2h \).

3. **New Volume Calculation**:
- The new volume \( V' \) is given by:
\[
V' = (2l) \times (2w) \times (2h)
\]
- This simplifies to:
\[
V' = 2l \times 2w \times 2h = 8 \times (l \times w \times h) = 8 \times V
\]
- Substituting the original volume:
\[
V' = 8 \times 15 \, \text{cubic feet} = 120 \, \text{cubic feet}
\]

Thus, the new volume of the box when each dimension is doubled is **120 cubic feet**.

The correct answer is **D. 120 cubic feet**.