Formulas for related rates

Pythagorean Theorem

The formula a² + b² = c² used to find the lengths of sides in a right triangle.

Area of a Rectangle

A = bh, where A is the area, b is the base, and h is the height.

Area of a Square

A = s², where A is the area and s is the length of a side.

Area of a Circle

A = πr², where A is the area and r is the radius.

Circumference of a Circle

C = 2πr, where C is the circumference and r is the radius.

Perimeter of a Rectangle

P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Perimeter of a Square

P = 4s, where P is the perimeter and s is the length of a side.

Volume of a Sphere

V = (4/3)πr³, where V is the volume and r is the radius.

Volume of a Cylinder

V = πr²h, where V is the volume, r is the radius, and h is the height.

Volume of a Cube

V = s³, where V is the volume and s is the length of a side.

Volume of a Rectangular Prism

V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

Surface Area of a Sphere

SA = 4πr², where SA is the surface area and r is the radius.

Surface Area of a Cube

SA = 6s², where SA is the surface area and s is the length of a side.

Surface Area of a Rectangular Prism

SA = 2lw + 2lh + 2wh, where SA is the surface area, l is the length, w is the width, and h is the height.