Find the percentage error in calculating the volume of a cubical box if an error if 1% is made in measuring the length of edges of the cube.

Options

A. `1%`
B. `2%`
C. `3%`
D. `3//2%`

Answer

C

Explanation

Let x be the length of an edge of the cube and y be its voulme. Then y= x^(3).
Let `Delta y` be the corresponding error in y. Then, `(Delta x)/x xx100=1 " "[Given]`
`rArr" "dx/x xx100=1" "[:'dx cong Delta x] ...(i)` We have to find `(Delta y)/yxx100.` Now, `y= x^(3) rArr dy/dx=3x^(2)`
`y= x^(3) rArr dy/dx=3x^(2)``:." " dy=dy/dxdx`
`rArr" "dy=3x^(2). dx rArrdy/y=(3x^(2))/ydx rArr dy/y=(3x^(2))/x^(3) dx" " [:' y=x^(3)]` `dy=3(dx)/x rArrdy/y xx100=3(dx/x xx100)=3" "["Using" (i)]`
`rArr" "(Delta y)/y xx100=3" "[:' dy cong Delta y]`
`rArr" "(Delta y)/y xx 100=3" "[:' dy cong Delta y]`
So, there is 3% error in calculating the volume of the cube.