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 $\pi \text{ m}^3$)

Let $y = f(x) = 2x^{2} - 3x + 2$. The differential of $y$ when $x$ changes from $2$ to $1.99$ is

If the semi-vertical angle of a cone is $45^{\circ}$ and its height is $20.025 \text{ cm}$,then the approximate value of its curved surface area (in $\text{sq. cm}$) is

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2 \%$.

The time $T$ of oscillation of a simple pendulum of length $L$ is governed by $T=2 \pi \sqrt{\frac{L}{g}}$,where $g$ is constant. The percentage by which the length must be changed in order to correct an error of loss equal to $2$ minutes of time per day is

If $y = x^3 + 5$ and $x$ changes from $3$ to $2.99$,then the approximate change in $y$ is