Find the volume and surface area of a rectangular box 2 ft by 1.3 ft by 4 ft.

Question

Question content area bottom
Part 1
The volume is
  
enter your response here
▼
feet
square feet
cubic feet
. ​(Simplify your​ answer.)

Answer 1

To find the volume \( V \) of a rectangular box, the formula is:

\[ V = \text{length} \times \text{width} \times \text{height} \]

Given the dimensions of the box as 2 ft (length), 1.3 ft (width), and 4 ft (height), the calculation would be:

\[ V = 2 , \text{ft} \times 1.3 , \text{ft} \times 4 , \text{ft} \]

Now, calculate the volume:

\[ V = 2 \times 1.3 \times 4 \] \[ = 2 \times 5.2 \] \[ = 10.4 , \text{cubic feet} \]

So the volume of the rectangular box is 10.4 cubic feet.

Now, for the surface area \( A \) of a rectangular box, the formula is:

\[ A = 2lw + 2lh + 2wh \]

Where:

• \( l \) is the length,
• \( w \) is the width,
• \( h \) is the height.

Plugging in the values:

\[ A = 2(2)(1.3) + 2(2)(4) + 2(1.3)(4) \]

Calculate each part:

1. \( 2(2)(1.3) = 5.2 \)
2. \( 2(2)(4) = 16 \)
3. \( 2(1.3)(4) = 10.4 \)

Now, sum these:

\[ A = 5.2 + 16 + 10.4 \] \[ = 31.6 , \text{square feet} \]

Thus, the surface area of the rectangular box is 31.6 square feet.

Summary:

• Volume: 10.4 cubic feet
• Surface Area: 31.6 square feet