The nearest approximate value of $\sqrt{2023}$ is

The approximate value of $\sqrt[3]{730}$ obtained by the application of derivatives is

The approximate value of $\cos \left(59^{\circ} 30^{\prime}\right)$ is (given $1^{\circ} = 0.0175^{c}, \sin 60^{\circ} = 0.8660$)

If the radius of a sphere is measured as $7 \text{ m}$ with an error of $0.02 \text{ m}$, then the approximate error in calculating its volume is (in $\pi \text{ m}^3$)

The radius and the height of a right circular solid cone are measured as $7 \text{ ft}$ each. If there is an error of $0.002 \text{ ft}$ for every foot in measuring them,then the error in the total surface area of the cone (in $\text{sq. ft}$) is:

$A$ point on the hypotenuse of a triangle is at distances $a$ and $b$ from the sides of the triangle. Show that the minimum length of the hypotenuse is $(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}$.