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Volume and surface areaGeometryMiddle schoolabout 1:03

Find the volume and surface area of a cone with radius 3 and height 4: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 12π ≈ 37.69911184 cubic units; surface area = 75.39822369 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 3 and height 4.
2. Step by step
1. $V = \frac{1}{3}\pi \cdot 3^2 \cdot 4 = 12\pi \approx 37.69911184$
  Volume: one third of the matching cylinder
2. $l = \sqrt{r^2 + h^2} = \sqrt{25} = 5$
  Slant height
3. $S = \pi \cdot 3^2 + \pi \cdot 3l \approx 75.39822369$
  Surface area: base plus lateral surface
3. The answer
$V = 12\pi \approx 37.69911184$
V = 12π ≈ 37.69911184, S = 75.39822369
4. Check
- Volume 37.69911184 and surface area 75.39822369 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a cone with radius 3 and height 4. 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 12pi approximately 37.69911184 cubic units; surface area equals 75.39822369 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 37.69911184 and surface area 75.39822369 are positive.

About volume and surface area

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