If the percentage error in the edge of a cube is 1, then error in its volume, is

Options

A. 0.01
B. `2%`
C. `3%`
D. none of these

Answer

C

Explanation

Let x be the lengthof an edge of the cube. Then, its volume y is given by `y=x^(3)`
Let `Delta x` be error in x and `Delta y` be the corresponding error in y. Then,
` rArr" "Delta y= dy/dx Deltax`
` Delta y=3x^(2)" "Deltax" "[:' y=x^(3) rArr dy/dx = 3x^(2)]`
`rArr" "(Deltay)/y = (3x^(2)" "Delta x)/y`
`rArr" "(Delta y)/y=(3x^(2)" "Delta x)/x^(3)`
`rArr" "(Delta y)/y xx 100=3 ((Delta x)/x xx100)=3% [:' (Delta x)/x xx100=1(Given)]`