If the error in measuring the diameter of a circle is $4\%$,the error in the radius of the circle would be (in $\%$)

The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2)^{\circ}C$ and $(82.3 \pm 0.3)^{\circ}C$. The rise in temperature with proper error limits is

Explain the statement: "The accuracy of a measurement cannot be determined by absolute error,but only by percentage error."

We measure the period of oscillation of a simple pendulum. In successive measurements,the readings turn out to be $2.63 \;s, 2.56 \;s, 2.42 \;s, 2.71 \;s$,and $2.80 \;s$. Calculate the absolute errors,relative error,and percentage error.

The outer and inner radii of a hollow cylinder are $(4.23 \pm 0.01) \text{ cm}$ and $(3.89 \pm 0.01) \text{ cm}$ respectively. What is the thickness of the wall of the cylinder?

$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$.
$Reason$ : The permissible error is calculated by the formula $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.