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Volume and surface areaGeometryMiddle schoolabout 0:51

Find the volume and surface area of a square pyramid with base side 10 and height 12: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 400 cubic units; surface area = 360 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 10 and height 12.
2. Step by step
1. $V = \frac{1}{3} \cdot 10^2 \cdot 12 = 400$
  Volume: one third of base area times height
2. $l = \sqrt{h^2 + (s/2)^2} = \sqrt{169} = 13$
  Slant height of each triangular face
3. $S = 10^2 + 2 \cdot 10l \approx 360$
  Surface area: base plus four triangles
3. The answer
$V = 400$
V = 400, S = 360
4. Check
- Volume 400 and surface area 360 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a square pyramid with base side 10 and height 12. 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 400 cubic units; surface area equals 360 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 400 and surface area 360 are positive.

About volume and surface area

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

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