Question

find the approximate change in the volume V of a cube of sides x meters caused by increasing the side by2%
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Answer 1

0.06x³ cubic metres

Step-by-step explanation:

Side of the cube = x metres

Side increased by 2% = 2 / 100 * x  

∆x = 0.02x meters

Volume of a cube = x³ cubic metres

To find the change in volume, ∆V:

 ∆V = dv / dx * (∆x)

 = d (x³) / dx * (∆x)

 = 3x² (0.02x)

= 0.06x³

So the approximate change in volume of a cube of side x, when the side is increased by 2% = 0.06x³ cubic metres.