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Cone Volume and Surface

Mensuration · Class VIII

Slide radius and height of a cone; see its slant, volume and surface area.

3 cm
type a value
120
4 cm
type a value
130
Live values
  • Slant l5
  • Volume37.6991
  • Curved surface area47.1239
  • Total surface area75.3982
xy
  • Volume vs radius (height fixed)

Formulas in this lab

  • Slant l
    r2+h2\sqrt{r^2 + h^2}
  • Volume
    13πr2h\tfrac{1}{3}\pi r^{2} h
  • Curved surface area
    πrl\pi r l
  • Total surface area
    πr(l+r)\pi r(l + r)
Tip: Volume is one-third pi r^2 h , a parabola in r when h is fixed.

Frequently asked questions

▶What are the volume and slant of a cone?

Volume is one-third pi r^2 h. Slant l = sqrt(r^2 + h^2). For r = 3 and h = 4, slant = 5 and volume = (1/3) * pi * 9 * 4 = about 37.7 cubic cm. The lab computes all three at once.

▶How do I use the cone volume lab?

Slide radius r and height h. The lab shows slant l, volume and curved surface pi r l. Try r = 6 and h = 8 to see slant 10, volume about 301.6 cubic cm and curved surface about 188.5 sq cm.

▶Where are cones found in real life?

Birthday party caps, ice-cream cones, kulfi moulds and the top of Hindu temples are all conical. A Diwali diya cap of base radius 2 cm and height 3 cm holds (1/3) pi * 4 * 3 = about 12.57 cubic cm of wax. The lab gives quick estimates for any cone.

▶Cone vs cylinder: same radius and height?

If a cone and cylinder share radius r and height h, the cone holds exactly one-third the volume. So a cylinder holding 300 ml has a matching cone of 100 ml. The lab shows the (1/3) factor at work: change r and h and compare with the cylinder lab numbers.