Question

Question
Sonjia has a box in the shape of a right rectangular prism. The box has a width of 5 cm. If the height of the box is 2 cm greater than the box’s length and the box’s length is 2 cm greater than the box’s width, what is the volume of the box?(1 point)
Responses

315 cm3
315 cm cubed

20 cm3
20 cm cubed

280 cm3
280 cm cubed

15 cm3

Answer 1

To find the volume of the box, we first need to determine its dimensions based on the relationships provided:

1. **Width of the box (W)**: 5 cm
2. **Length of the box (L)** is 2 cm greater than the width:
\[
L = W + 2 = 5 + 2 = 7 \text{ cm}
\]
3. **Height of the box (H)** is 2 cm greater than the length:
\[
H = L + 2 = 7 + 2 = 9 \text{ cm}
\]

Now we have:
- Width (W) = 5 cm
- Length (L) = 7 cm
- Height (H) = 9 cm

The volume \( V \) of a right rectangular prism is calculated as:
\[
V = L \times W \times H
\]
Substituting the values we found:
\[
V = 7 \times 5 \times 9
\]

Calculating it step by step:
1. \( 7 \times 5 = 35 \)
2. \( 35 \times 9 = 315 \)

Thus, the volume of the box is:
\[
\text{Volume} = 315 \text{ cm}^3
\]

Therefore, the answer is:
**315 cm³ (315 cm cubed)**.