Solve a problem

Volume and surface areaGeometryMiddle schoolabout 1:03

Find the volume and surface area of a cylinder with radius 2 and height 5: animated lesson

A narrated, step-by-step volume and surface area video lesson with captions. Final answer: Volume = 20π ≈ 62.83185307 cubic units; surface area = 28π ≈ 87.9645943 square units.

SpeedLanguage

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 2 and height 5.
2. Step by step
1. $V = \pi \cdot 2^2 \cdot 5 = 20\pi \approx 62.83185307$
  Volume: base area times height
2. $S = 2\pi \cdot 2^2 + 2\pi \cdot 2 \cdot 5 = 28\pi \approx 87.9645943$
  Surface area: two circles plus the curved side
3. The answer
$V = 20\pi \approx 62.83185307$
V = 20π ≈ 62.83185307, S = 28π ≈ 87.9645943
4. Check
- Volume 62.83185307 and surface area 87.9645943 are positive.

Transcript

The problem. Here is the problem: Find the volume and surface area of a cylinder with radius 2 and height 5. 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 20pi approximately 62.83185307 cubic units; surface area equals 28pi approximately 87.9645943 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 62.83185307 and surface area 87.9645943 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 cylinder with radius…