Question

The edge of a cube measures `3.5 \times 10^-2` meters. What is the volume of the cube in cubic meters in scientific notation?

Answer 1

See a solution process below:

Explanation:

The formula for the volume of a cube is:

`V = s^2 = s * s * s`

Where: `s` is the length of the side of the cube.

Substituting `(3.5 xx 10^02)` for `s` gives:

`V = (3.5 xx 10^-2)"m" xx (3.5 xx 10^-2)"m" xx (3.5 xx 10^-2)"m"`

We can rewrite this as:

`V = (3.5 xx 3.5 xx 3.5) xx (10^-2 xx 10^-2 xx 10^-2) xx ("m" xx "m" xx "m")`

`V = (12.25 xx 3.5) xx 10^(-2 - 2 - 2) xx "m"^3`

`V = 42.875 xx 10^-6"m"^3`

To write this in scientific notation we need to move the decimal point 1 place to the left so we need to add 1 to the exponent for 10s term:

`V = 4.2875 xx 10^(-6 + 1)"m"^3`

`V = 4.2875 xx 10^-5"m"^3`