WEBVTT

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Here is the problem: Find the volume and surface area of a cone with radius 5 and height 12.

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Compute the volume (cubic units) and total surface area (square units) of the solid from its dimensions in one length unit.

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Volume: one third of the matching cylinder.

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Slant height.

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Surface area: base plus lateral surface.

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So the answer is Volume equals 100pi approximately 314.1592654 cubic units; surface area equals 282.7433388 square units.

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Volume counts unit cubes inside a solid; surface area counts unit squares needed to wrap it. Doubling every length multiplies volume by 8 and surface area by 4.

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Volume 314.1592654 and surface area 282.7433388 are positive.