The relative error in the dertmination o...

The relative error in the dertmination of the surface area of a sphere is `alpha`. Then the relative error in the determination of its volume is :

`(3)/(2)alpha`

`(2)/(3)alpha`

`alpha`

`(5)/(2)alpha`

Text Solution

Verified by Experts

The correct Answer is:

Surface area of sphere is `S= 4pi r^(2)`
`(triangleS)/(S)=2xx(triangle r)/(r )=alpha`
`implies (triangle r)/(r )=(alpha)/(2)" ""………….."(i)`
Volume of sphere `v=(4)/(3)pi r^(3)`
`implies (triangleV)/(V)=3xx(triangle r)/(r )`
Substituting from equation (i) we get the following :
`(triangleV)/(V)=(3)/(2)alpha`

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The relative error in the determination of the surface area of a sphere is alpha . Then the relative error in the determination of its volume is :

`5/2alpha`

`alpha`

`2/3 alpha`

`3/2 alpha`

The relative error in the measurement of the side of a cube is 0.027 The relative error in the measurement of its volume is

`0.027`

`0.054`

`0.081`

`0.046`

If the surface area of a sphere is (144 pi)m^(2) then its volume is

`(288pi)m^(3)`

`(188 pi)m^(3)`

`(300 pi)m^(3)`

`(316pi) m^(3)`