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Volume and surface areaGeometryMiddle schoolabout 1:08

Find the volume and surface area of a cylinder with radius 4 and height 9: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 144π ≈ 452.3893421 cubic units; surface area = 104π ≈ 326.725636 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 cylinder with radius 4 and height 9.
2. Step by step
1. $V = \pi \cdot 4^2 \cdot 9 = 144\pi \approx 452.3893421$
  Volume: base area times height
2. $S = 2\pi \cdot 4^2 + 2\pi \cdot 4 \cdot 9 = 104\pi \approx 326.725636$
  Surface area: two circles plus the curved side
3. The answer
$V = 144\pi \approx 452.3893421$
V = 144π ≈ 452.3893421, S = 104π ≈ 326.725636
4. Check
- Volume 452.3893421 and surface area 326.725636 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a cylinder with radius 4 and height 9. 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: base area times height. Surface area: two circles plus the curved side.

The answer. So the answer is Volume equals 144pi approximately 452.3893421 cubic units; surface area equals 104pi approximately 326.725636 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 452.3893421 and surface area 326.725636 are positive.

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