High School

1 m is equivalent to 3.281 ft. A cube with an edge of 1.5 ft has a volume of:

A) 10.5 m³
B) 1.2 × 10² m³
C) 9.5 × 10^(-2) m³
D) 0.21 m³
E) 9.6 × 10^(-2) m³

Answer :

To determine the volume of a cube with an edge length of 1.5 feet in cubic meters, we need to follow these steps:

  1. Find the volume of the cube in cubic feet.

    • The formula for the volume of a cube is [tex]V = a^3[/tex], where [tex]a[/tex] is the edge length of the cube.
    • Here, [tex]a = 1.5[/tex] feet.
    • So, [tex]V = (1.5)^3 = 3.375[/tex] cubic feet.

  2. Convert the volume from cubic feet to cubic meters.

    • We know that [tex]1[/tex] meter [tex]= 3.281[/tex] feet.
    • Therefore, to convert feet to meters, we divide by [tex]3.281[/tex].
    • Thus, to convert cubic feet to cubic meters, we use the conversion factor [tex](\frac{1}{3.281})^3.[/tex]

  3. Calculate the conversion.

    • [tex]3.375 \text{ ft}^3 \times \left(\frac{1}{3.281}\right)^3 \approx 0.0959 \text{ m}^3.[/tex]

Therefore, the volume of the cube with an edge of 1.5 feet is approximately [tex]0.0959 \text{ m}^3.[/tex] This corresponds to option E) 9.6 \times 10^{-2} \text{ m}^3.

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