Question

the volume of the box is 18 cubic centimeters. the box is 3 centimeters long and 3 centimeters tall. what is the width of the box, in centimeters?
green box image
small green cube = 1 cubic centimeter
options: 3, 6, 2, 10

Explanation:

Step1: Recall the volume formula for a rectangular box

The volume \( V \) of a rectangular box (a rectangular prism) is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Plug in the known values and solve for \( w \)

We know that \( V = 18 \) cubic centimeters, \( l = 3 \) centimeters, and \( h = 3 \) centimeters. Substituting these values into the formula, we get:

$$ 18 = 3 \times w \times 3 $$

First, simplify the right - hand side: \( 3\times3\times w=9w \). So the equation becomes \( 18 = 9w \).
To solve for \( w \), we divide both sides of the equation by 9: \( w=\frac{18}{9}=2 \). Wait, but let's check the options again. Wait, maybe I misread the height. Wait, the problem says "3 centimeters tall"? Wait, no, maybe the height is 1? Wait, no, the original problem: "The volume of the box is 18 cubic centimeters. The box is 3 centimeters long and 3 centimeters tall. What is the width of the box, in centimeters?" Wait, no, if \( l = 3 \), \( h = 3 \), then \( V=l\times w\times h\Rightarrow18 = 3\times w\times3\Rightarrow18 = 9w\Rightarrow w = 2 \). But the options are 3, 6, 2, 10? Wait, maybe the height is 1? Wait, maybe I made a mistake. Wait, let's re - examine. Wait, the small cube is 1 cubic centimeter, so its side length is 1. The big box: length is 3 (so 3 small cubes along length), height is 3 (3 small cubes along height)? No, if the volume is 18, and length is 3, height is 3, then width is \( 18\div(3\times3)=2 \). So the width is 2.

Answer:

2 (assuming the option with 2 is one of the choices, looking at the options given as 3, 6, 2, 10, the correct option is the one with 2)