equations for calc related rates and other thing i forgor the name of

Volume of a cube with side length $s$

$$V = s^3$$

Surface area of a cube with side length $s$

$$A = 6s^2$$

Volume of a sphere with radius $r$

$$V = \frac{4}{3}\pi r^3$$

Surface area of a sphere with radius $r$

$$A = 4\pi r^2$$

Volume of a right circular cone with radius $r$ and height $h$

$$V = \frac{1}{3}\pi r^2 h$$

Key strategy for related rates problems involving a cone with changing radius and height

Use similar triangles ($\frac{r}{h} = \text{ratio}$) to substitute out one variable before differentiating.

Volume of a cylinder with radius $r$ and height $h$

$$V = \pi r^2 h$$

Area of an equilateral triangle with side length $s$

$$A = \frac{\sqrt{3}}{4} s^2$$

Pythagorean Theorem relating legs $x, y$ and hypotenuse $z$

$$x^2 + y^2 = z^2$$

Area of an annulus (region between concentric circles of radii $R$ and $r$ where $R > r$)

$$A = \pi R^2 - \pi r^2$$

Total perimeter of an annulus with outer radius $R$ and inner radius $r$

$$P = 2\pi R + 2\pi r$$

Linear approximation formula for $f(x)$ at $x = a$

$$L(x) = f(a) + f'(a)(x - a)$$

Differential error formula for a function $y = f(x)$

$$dy = f'(x)\,dx$$

Percentage error formula using differentials

$$\left|\frac{\text{Actual} - \text{Estimated}}{\text{Actual}}\right| \times 100\% \quad \text{or} \quad \frac{dy}{y} \times 100\%$$