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Volume and surface areaGeometryMiddle schoolabout 1:07

Find the volume and surface area of a sphere with radius 3: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 36π ≈ 113.0973355 cubic units; surface area = 36π ≈ 113.0973355 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 sphere with radius 3.
2. Step by step
1. $V = \frac{4}{3}\pi \cdot 3^3 = 36\pi \approx 113.0973355$
  Volume
2. $S = 4\pi \cdot 3^2 = 36\pi \approx 113.0973355$
  Surface area
3. The answer
$V = 36\pi \approx 113.0973355$
V = 36π ≈ 113.0973355, S = 36π ≈ 113.0973355
4. Check
- Volume 113.0973355 and surface area 113.0973355 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a sphere with radius 3. 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. Surface area.

The answer. So the answer is Volume equals 36pi approximately 113.0973355 cubic units; surface area equals 36pi approximately 113.0973355 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 113.0973355 and surface area 113.0973355 are positive.

About volume and surface area

Volume and surface area of prisms, cylinders, cones and spheres.

Find the volume and surface area of a sphere with radius 3