1.

The height of a cylinder is equal to the radius. If an error of `alpha%`is made in the height, then percentage error in its volume is`alpha%`(b) 2`alpha%`(c) 3`alpha%`(d) none of these

Answer» height of cyliner is h & radius is r
so,`h=r`
`(del h)/h xx 100 = a`
`(dh)/h xx 100 = a`
`dh = (ah)/100`
volume of cylinder= `v= pi r^2 h= pi h^2 h = pi h^3`
`v = pi h^3`
diff wrt h
`(dv)/(dh) = 3 pi h^2 `
`dv = 3 pi h^2 *dh`
`(dv)/v xx 100 = (dv)/v xx 100 = (3 pi h^2 *dh)/(pi h^3) xx 100`
`(dv)/v xx 100= 3a `
correct option is c


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