Question

which box has a volume of 125 cubic feet? (with images of boxes with dimensions: one with 12 feet, 5 feet, 2 feet; one with 5 feet, 5 feet, 5 feet; one with 4 feet, 4 feet, 4 feet; one with 4 feet, 5 feet, 6 feet)

Explanation:

Step1: Recall Volume Formula

For a rectangular prism (box), volume \( V = l \times w \times h \). For a cube (special case, \( l = w = h \)), \( V = s^3 \) (where \( s \) is side length).

Step2: Calculate Volume of Each Box

• Top - Left Box: \( l = 12 \), \( w = 2 \), \( h = 5 \). \( V = 12 \times 2 \times 5 = 120 \) cubic feet.
• Top - Right Box (Cube): \( s = 5 \). \( V = 5^3 = 125 \) cubic feet.
• Bottom - Left Box (Cube): \( s = 4 \). \( V = 4^3 = 64 \) cubic feet.
• Bottom - Right Box: \( l = 5 \), \( w = 5 \), \( h = 4 \). \( V = 5 \times 5 \times 4 = 100 \) cubic feet.

Answer:

The top - right box (with side length 5 feet for all dimensions) has a volume of 125 cubic feet.