The triangle is 1/2 of a rectangle so why is the cone 1/3 of a cylinder? @blackpenredpen

Uploaded August 2026 | Updated September 2026, 3 weeks ago

We will see why the volume of a cone is 1/3 of the cylinder with the same base and height. First we will do a "water proof", then we will see how to use the disk method to compute the volume of the revolution of the solid. Great lesson for calculus 1 and AP calculus students.

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The triangle is 1/2 of a rectangle so why is the cone 1/3 of a cylinder?

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$First time solving an A-Level maths exam! (90 minutes, uncut) I will be doing a British A-Level further maths paper on the spot for the first time! This paper contains mainly algebra and calculus. Topics include complex numbers, hyperbolic equations, exponential equations, trigonometric identities and equations, first-order linear differential equations, determinant and the inverse of a 3x3 matrix, and more! Was I able to solve all the questions within 90 minutes? Was I able to get all the questions correct? Watch to find out. The afterward https://youtu.be/9GFUyT-D6D0 Try the paper first: https://qualifications.pearson.com/content/dam/pdf/A-Level/Mathematics/2017/Exam-materials/9fm0-01-que-20220526.pdf Big thanks to my Patrons for the full-marathon support! Ben D, Grant S, Erik S. Mark M, Phillippe S., Nicole D. 💪 Support this channel and get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 Timestamps: 0:00 A-Level further math paper from June 2022 0:58 Q1 Solving a cubic equation with complex roots 6:23 Q2 Solving a 4-th degree hyperbolic equation 15:55 Q3 Solving a first-order linear differential equation with integrating factor 21:28 Q4 Solving a series problem with natural log 28:55 Q5 Finding the determinant and the inverse of a 3x3 matrix Correction to Q5: https://youtu.be/pXdEBA6xI1c?si=11CZl3RkNheQQvMR 40:50 Q6 Partial fraction decomposition & integral of a rational function 50:05 Q7 A complex number problem 1:00:11 Q8 A long trig identity 1:23:39 Q9 An improper integral with hyperbolic cosine$