A family size Cheerios box is in the shape of a right rectangular prism with dimensions 9 in by 12 in by 2.5 in. Find its volume.

A. [tex]\(24.5 \, \text{in}^3\)[/tex]
B. [tex]\(344 \, \text{in}^3\)[/tex]
C. [tex]\(292.5 \, \text{in}^3\)[/tex]
D. [tex]\(585 \, \text{in}^3\)[/tex]



Answer :

To find the volume of a right rectangular prism, you multiply its length, width, and height. The problem states that the dimensions of the Cheerios box are 18 inches in length, 9 inches in width, and 2.5 inches in height.

Step-by-step solution:

1. Identify the dimensions of the prism:
- Length ([tex]\( l \)[/tex]) = 18 inches
- Width ([tex]\( w \)[/tex]) = 9 inches
- Height ([tex]\( h \)[/tex]) = 2.5 inches

2. Apply the formula for the volume of a rectangular prism:
[tex]\[ \text{Volume} = l \times w \times h \][/tex]

3. Substitute the given dimensions into the formula:
[tex]\[ \text{Volume} = 18 \, \text{in} \times 9 \, \text{in} \times 2.5 \, \text{in} \][/tex]

4. Calculate the product:
[tex]\[ \text{Volume} = 405 \, \text{in}^3 \][/tex]

Thus, the volume of the Cheerios box is [tex]\( 405 \, \text{in}^3 \)[/tex].

However, the choices provided seem to give units of square inches (in²), which is incorrect for volume. Correcting this, the volume should be measured in cubic inches (in³), and the correct volume of the box, based on the choices, is:

None of the provided answers (A, B, C, D) are correct as they all indicate square inches rather than cubic inches. The definitive volume, presented correctly, is [tex]\( 405 \, \text{in}^3 \)[/tex].

But given the format of the choices and the likely typographical error in unit representation:

- Correct answer should read:
- [tex]\( 405 \, \text{in}^3 \)[/tex].