Assertion: The error in the measurement of radius of sphere is `0.3%`. The permissible error in its surface area is `0.6 %`.
Reason: The permissible error is calculated by the formula `(Delta A)/(A) = (4 Delta r)/( r)`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

C

Explanation

`A = 4 pi r^2` (error will not be involved in constant `4 pi`)
Fractional error `(Delta A)/(A) = (2 Delta r)/(r )`
`(Delta A)/(A) xx 100 = 2 xx 0.3 % = 0.6 %`
but `(Delta A)/(A) = (4 Delta r)/( r)` is false.