What is the maximum volume of cone which is inscribed in a cylinder where radius of cylinder is 4cm and height is 7cm?

This cone volume calculator can help in solving your math problems or can answer your weird day-to-day questions. How much ice cream fits into my cone? How much cream can I put into the pastry bag? Or what's the volume of my conical champagne glass? If these are the questions that you would like answered, keep reading!

A cone is a solid that has a circular base and a single vertex. To calculate its volume, you need to multiply the base area (area of a circle: π * r²) by height and by 1/3:

• volume = (1/3) * π * r² * h

A cone with a polygonal base is called a pyramid.

Let's calculate how much water fits into the conical part of the funnel.

1. Determine the height of the cone. For our funnel, it's 4 in.
2. Enter the base radius. It may be equal to 3 in.
3. The calculator now displays the volume of the cone - in our case, it's 37.7 cu in.

Remember that you can change the units to meet your exact needs - click on the unit and select it from the list. Check out our volume converter tool if you need a simple volume unit conversion.

A truncated cone is the cone with the top cut off, with a cut perpendicular to the height. You can calculate frustum volume by subtracting the smaller cone volume (the cut one) from the bigger cone volume (base one) or use the formula:

• volume = (1/3) * π * depth * (r² + r * R + R²), where R is a radius of the base of a cone, and r of top surface radius

An example of the volume of a truncated cone calculation can be found in our potting soil calculator, as the standard flower pot is a frustum of a cone.

An oblique cone is a cone with an apex that is not aligned above the center of the base. It "leans" to one side, similarly to the oblique cylinder. The cone volume formula of the oblique cone is the same as for the right one.

To calculate the volume of a cone, follow these instructions:

1. Find the cone's base area a. If unknown, determine the cone's base radius r.
2. Find the cone's height h.
3. Apply the cone volume formula: volume = (1/3) * a * h if you know the base area, or volume = (1/3) * π * r² * h otherwise.
4. Congratulations, you've successfully computed the volume of your cone!

If a cone and cylinder have the same height and base radius, then the volume of a cone is equal to one-third of that of the cylinder. That is, you would need the contents of three cones to fill up this cylinder. The same relationship holds for the volume of a pyramid and that of a prism (given that they have the same base area and height).

The size of an ice cream waffle varies quite widely, yet there are a few sizes that are typical:

Recall that the cone volume formula reads:

volume = (1/3) * π * r² * h

So in our case, we have:

volume = (1/3) * π * 1² * 3,

So the volume of our cone is exactly π! As we all know, this can be approximated as volume ≈ 3.14159.

Get a Widget for this Calculator

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

🏠

Subjects

➗

🧪

🏛️

📺

🤝

💻

💰

📚

Resources

📓

🏆

💯

❓

🔀

🎒

🎒