Question

Find the approximation change in the volume V of a cube of side X meters caused by increasing the side by 2% ., ​

Answer 1

Cube

CubeSolve for volume

CubeSolve for volumeV=8

CubeSolve for volumeV=8a Edge

CubeSolve for volumeV=8a Edge 2

Answer 2

Hi

Solution:- given , ∆x = 2% of x = 2x/100 = 0.02x

The volume of the cube V = x³

dv/dx = db/dx = ∆x = 3x²*∆x = 3*x²(0.02x) = 0.06x³

Hence ,the approximate value changes in volume = 0.06x³m³

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