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Cylinder Volume and Surface

Mensuration · Class VIII

Choose radius and height; see volume, lateral surface and total surface area.

4 cm
type a value
120
10 cm
type a value
130
Live values
  • Volume502.6548
  • Curved surface area251.3274
  • Total surface area351.8584
xy
  • Volume vs radius (height fixed)

Formulas in this lab

  • Volume
    πr2h\pi r^{2} h
  • Curved surface area
    2πrh2\pi r h
  • Total surface area
    2πr(r+h)2\pi r(r + h)
Tip: V = pi r^2 h , a quadratic in r, so doubling the radius gives four times the volume.

Frequently asked questions

▶What is the volume and surface formula of a cylinder?

Volume is pi r^2 h. Curved (lateral) surface is 2 pi r h. Total surface is 2 pi r (r + h). For r = 4 cm and h = 10 cm, V is about 502.65 cubic cm and curved surface about 251.33 sq cm.

▶How do I use the cylinder volume lab?

Slide radius r and height h. The lab shows volume, curved surface and total surface area. Try r = 7 and h = 14 to see V about 2155 cubic cm; pi is taken as the precise constant, not just 22/7.

▶How is cylinder volume useful for Indian water tanks?

Plastic Sintex water tanks are cylinders. A tank of radius 50 cm and height 100 cm holds pi * 50^2 * 100 = 785000 cubic cm or 785 litres. The lab uses cm, so multiply your answer by 1/1000 to get litres.

▶Curved surface vs total surface: which to use?

Curved surface is the side only (label area on a tin can). Total surface adds both circular ends (paint a closed drum). For a Rs 100 paint job, use curved surface for open tanks and total for closed ones. The lab shows both so you can pick.