To determine the volume of the box, let's go through the process step-by-step.
### Step 1: Identify the dimensions of the box
The given dimensions are:
- Length ([tex]\( l \)[/tex]): 15 inches
- Width ([tex]\( w \)[/tex]): 8 inches
- Height ([tex]\( h \)[/tex]): 8 inches
### Step 2: Calculate the area of the base
The area of the base ([tex]\( B \)[/tex]) is obtained by multiplying the length and the width of the base of the box. Therefore:
[tex]\[ B = l \times w \][/tex]
Substituting the given values:
[tex]\[ B = 15 \, \text{inches} \times 8 \, \text{inches} = 120 \, \text{square inches} \][/tex]
So the area of the base, [tex]\( B \)[/tex], is [tex]\( 120 \, \text{square inches} \)[/tex].
### Step 3: Calculate the volume of the box
The volume of the box ([tex]\( V \)[/tex]) can be calculated by multiplying the area of the base [tex]\( B \)[/tex] by the height [tex]\( h \)[/tex]. Therefore:
[tex]\[ V = B \times h \][/tex]
Substituting the values of [tex]\( B \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ V = 120 \, \text{square inches} \times 8 \, \text{inches} = 960 \, \text{cubic inches} \][/tex]
### Final Answers
- The area of the base of the box ([tex]\( B \)[/tex]) is [tex]\( 120 \, \text{square inches} \)[/tex]
- The volume of the box ([tex]\( V \)[/tex]) is [tex]\( 960 \, \text{cubic inches} \)[/tex]
The area of the base of the box, [tex]\( B \)[/tex], is [tex]\( 120 \, \text{in}^2 \)[/tex].
The volume of the box is [tex]\( 960 \, \text{in}^3 \)[/tex].
