The approximate value of $\sin 31^{\circ}$ is

The semi-vertical angle of a right circular cone is $45^{\circ}$. If the radius of the base of the cone is measured as $14 \text{ cm}$ with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \text{ cm}$,then the approximate error in measuring its total surface area is (in $\text{sq. cm}$):

The side of an equilateral triangle is $5$ units. In measuring the side, an error of $0.05$ units is made. Then the percentage error in measuring the area of the triangle is

The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ} = 0.0174$ radians and $\sqrt{3} = 1.732$ is

The approximate value of $\tan ^{-1}(0.999)$ is (use $\pi=3.1415$ )

The approximate value of $(1.0002)^{3000}$ is