Question

The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is

Options

• `0.06  x^3m^3`

• `0.6  x^3m^3`

• `0.09  x^3m^3`

• `0.9  x^3m^3`

Answer 1

`0.09  x^3m^3`

Explanation:

Side of a cube = `x` meters.

Volume of cube = `x^3`

For `Δx`, ∴ 3% of `x = 0.3x`

Let ΔV be the change = Δv volume

ΔV = `(dv)/(dx) xx Δx = 3x^2 xx Δx`

But `Δx = 0.03x`

ΔV = `.03x`

∴ ΔV = `3x^2 xx 0.03x = 0.09x^3m^3`