What is the total surface area of a cone whose height is 48 cm and area of the base of the cone is 616 sq cm?

Let the radius of base and slant height of the cone be r cm and l cm, respectively.Slant height of the cone = 3 × Radius of the cone         (Given)∴ l = 3r       

Total surface area of the cone = 616 cm2

⇒ `22/7` x r x ( r + 3r ) = 616

⇒ `22/7` x r x 4r = 616

⇒ `88/7`r2 =616

⇒ r2 =` [616  xx 7 ]/88` = 49

⇒ r = `sqrt 49` = 7cm'

∴ Slant height of the cone, l = 3r = 3 × 7 = 21 cm
Thus, the slant height of the cone is 21 cm.

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π = pi = 3.1415926535898

Calculator Use

This online calculator will calculate the various properties of a right circular cone given any 2 known variables. The term "circular" clarifies this shape as a pyramid with a circular cross section. The term "right" means that the vertex of the cone is centered above the base. Using the term "cone" by itself often commonly means a right circular cone.

Units: Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. For example, if you are starting with mm and you know r and h in mm, your calculations will result with s in mm, V in mm3, L in mm2, B in mm2 and A in mm2.

Below are the standard formulas for a cone. Calculations are based on algebraic manipulation of these standard formulas.

Circular Cone Formulas in terms of radius r and height h:

• Volume of a cone:
• Slant height of a cone:
• Lateral surface area of a cone:
• Base surface area of a cone (a circle):
• Total surface area of a cone:
  • A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

Circular Cone Calculations:

Use the following additional formulas along with the formulas above.

• Given radius and height calculate the slant height, volume, lateral surface area and total surface area.
  Given r, h find s, V, L, A
• Given radius and slant height calculate the height, volume, lateral surface area and total surface area.
  Given r, s find h, V, L, A
• Given radius and volume calculate the height, slant height, lateral surface area and total surface area.
  Given r, V find h, s, L, A
• Given radius and lateral surface area calculate the height, slant height, volume and total surface area.
  Given r, L find h, s, V, A
  • s = L / (πr)
  • h = √(s2 - r2)
• Given radius and total surface area calculate the height, slant height, volume and lateral surface area.
  Given r, A find h, s, V, L
  • s = [A - (πr2)] / (πr)
  • h = √(s2 - r2)
• Given height and slant height calculate the radius, volume, lateral surface area and total surface area.
  Given h, s find r, V, L, A
• Given height and volume calculate the radius, slant height, lateral surface area and total surface area.
  Given h, V find r, s, L, A
  • r = √[ (3 * v) / (π * h) ]
• Given slant height and lateral surface area calculate the radius, height, volume, and total surface area.
  Given s, L find r, h, V, A
  • r = L / (π * s)
  • h = √(s2 - r2)

References

Weisstein, Eric W. "Cone." From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/Cone.html