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Volume and surface areaGeometryMiddle schoolabout 1:04

Find the volume and surface area of a cone with radius 5 and height 12: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 100π ≈ 314.1592654 cubic units; surface area = 282.7433388 square units.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Find the volume and surface area of a cone with radius 5 and height 12.
2. Step by step
1. $V = \frac{1}{3}\pi \cdot 5^2 \cdot 12 = 100\pi \approx 314.1592654$
  Volume: one third of the matching cylinder
2. $l = \sqrt{r^2 + h^2} = \sqrt{169} = 13$
  Slant height
3. $S = \pi \cdot 5^2 + \pi \cdot 5l \approx 282.7433388$
  Surface area: base plus lateral surface
3. The answer
$V = 100\pi \approx 314.1592654$
V = 100π ≈ 314.1592654, S = 282.7433388
4. Check
- Volume 314.1592654 and surface area 282.7433388 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a cone with radius 5 and height 12. Compute the volume (cubic units) and total surface area (square units) of the solid from its dimensions in one length unit.

Step by step. Volume: one third of the matching cylinder. Slant height. Surface area: base plus lateral surface.

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

Check. Volume 314.1592654 and surface area 282.7433388 are positive.

About volume and surface area

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