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Volume and surface areaGeometryMiddle schoolabout 0:50

Find the volume and surface area of a square pyramid with base side 6 and height 4: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 48 cubic units; surface area = 96 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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Find the volume and surface area of a square pyramid with base side 6 and height 4.
2. Step by step
1. $V = \frac{1}{3} \cdot 6^2 \cdot 4 = 48$
  Volume: one third of base area times height
2. $l = \sqrt{h^2 + (s/2)^2} = \sqrt{25} = 5$
  Slant height of each triangular face
3. $S = 6^2 + 2 \cdot 6l \approx 96$
  Surface area: base plus four triangles
3. The answer
$V = 48$
V = 48, S = 96
4. Check
- Volume 48 and surface area 96 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a square pyramid with base side 6 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 base area times height. Slant height of each triangular face. Surface area: base plus four triangles.

The answer. So the answer is Volume equals 48 cubic units; surface area equals 96 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 48 and surface area 96 are positive.

About volume and surface area

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

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