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Volume and surface areaGeometryMiddle schoolabout 1:06

Find the volume and surface area of a hemisphere with radius 4: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 128π/3 ≈ 134.0412866 cubic units; surface area = 48π ≈ 150.7964474 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 hemisphere with radius 4.
2. Step by step
1. $V = \frac{2}{3}\pi \cdot 4^3 = \frac{128\pi}{3} \approx 134.0412866$
  Volume: half a sphere
2. $S = 2\pi r^2 + \pi r^2 = 3\pi \cdot 4^2 = 48\pi \approx 150.7964474$
  Surface area: curved half plus the flat disc
3. The answer
$V = \frac{128\pi}{3} \approx 134.0412866$
V = 128π/3 ≈ 134.0412866, S = 48π ≈ 150.7964474
4. Check
- Volume 134.0412866 and surface area 150.7964474 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a hemisphere with radius 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: half a sphere. Surface area: curved half plus the flat disc.

The answer. So the answer is Volume equals 128pi/3 approximately 134.0412866 cubic units; surface area equals 48pi approximately 150.7964474 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 134.0412866 and surface area 150.7964474 are positive.

About volume and surface area

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