How to Calculate Volume and Surface Area of a Cone

The Organic Chemistry Tutor

This educational video provides a step-by-step tutorial on calculating the volume, lateral area, and total surface area of a cone. The instructor begins by defining the geometric properties of a cone, including radius, height, and slant height, and explains the mathematical relationship between these dimensions using the Pythagorean theorem. The video clearly derives and lists the specific formulas required for each calculation: V = (1/3)πr²h for volume, LA = πrl for lateral area, and SA = πr² + πrl for surface area. The content progresses through three distinct practice problems that increase in complexity. The first example is a straightforward application where the radius and height are given, requiring students to find the slant height first. The second example provides the radius and slant height, challenging students to work backward to find the height before calculating volume. The final example introduces diameter, requiring students to first determine the radius. Each problem emphasizes proper unit notation (cubic units for volume vs. square units for area). This video is an excellent resource for geometry students learning to work with 3D solids. It is particularly useful for teachers to assign as a flipped classroom lesson or for students needing remediation on using the Pythagorean theorem within 3D contexts. The clear, handwritten demonstration style allows students to follow the procedural logic of substituting values into formulas and solving algebraic equations step-by-step.