Cylinders: Volume and Surface Area

Geometry · Axiom Academy

LESSON Cylinders: Volume and Surface Area Measuring circular prisms — where the round base turns every formula into a story about . 1. A Cylinder Is a Circle, Extruded Start with a single circular base of radius r . Lift a copy of it straight up through a height h , and the path it sweeps out is the cylinder. That is why the volume is just the base area multiplied by the height — a stack of circles, h tall. Two circles + the rectangular wrapper The surface area has three parts: the top circle, the bottom circle, and the curved side. The trick is the side. Peel it off and flatten it — it unrolls into a perfect rectangle whose width is the circle's circumference and whose height is h . So the lateral area is . A cylinder has radius 5 cm and height 12 cm. Find its volume. (Use .) 4. Example: Finding Surface Area Find the surface area of a cylinder with radius 4 in and height 10 in. (Use .) 5. Example: Finding Radius from Volume A cylinder has volume 502.4 m³ and height 10 m. Find the radius. (Use .) You've seen a cylinder as a circle given depth, unrolled its curved side into a flat rectangle, and used both formulas on three problems. The key takeaways: Scroll up to revisit any step.

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