Question

A shipping company sells large boxes and small boxes. The dimensions of the large box are 3 times the dimensions of the small box.



How does the volume of the large box compare to the volume of the small box?

Answer options with 4 options
A.
The volume of the large box is 3 times the volume of the small box.

B.
The volume of the large box is 6 times the volume of the small box.

C.
The volume of the large box is 9 times the volume of the small box.

D.
The volume of the large box is 27 times the volume of the small box.

Answer 1

To find out how the volume of the large box compares to the volume of the small box, we need to compare their volumes based on their dimensions.

Let the dimensions of the small box be \( l \), \( w \), and \( h \) (length, width, height).

The volume of the small box \( V_s \) is given by:

\[
V_s = l \times w \times h
\]

The dimensions of the large box are 3 times those of the small box, so the dimensions of the large box are \( 3l \), \( 3w \), and \( 3h \).

The volume of the large box \( V_l \) is given by:

\[
V_l = (3l) \times (3w) \times (3h)
\]

Calculating \( V_l \):

\[
V_l = 27 \times (l \times w \times h)
\]
\[
V_l = 27 \times V_s
\]

This shows that the volume of the large box is 27 times the volume of the small box.

Therefore, the correct answer is:

**D. The volume of the large box is 27 times the volume of the small box.**