The concepts of cone volume and cubic feet in mathematics


Suppose you want to know how many beans will fit inside a cylindrical jar, or how many pencils will fit inside the box it means that you need to know the volume. In simple words, if one wants to know the amount of space something will take up, he/she just measure the volume of a three-dimensional object. 

Volume is the basic characteristic of all three-dimensional objects. When talking about volume, it is also important to discuss the method of measuring it. Commonly a measuring cylinder is used to measure the volume of solid shapes.

Basic procedure to measure the volume

We take a cylinder, filled with water, and note down the reading of the measuring cylinder; this is your V1. Now, take your object and dip it into the water, after dipping it note down the reading of the displaced water, this will be known as V2. 

At the end of this process we devise a formula that is; 

The volume of the object = V2 – V1

We put in the values and calculate them. The answer will be our desired value, which is the volume of the solid object.

Volume in mathematics

Volume in mathematics is more or less defined in the same way. But the method for measuring the volume of various figures and objects is different. Mathematical formulas are used to calculate the volume of diagrams and figures provided.

We may take an example of a dice. The shape of dice, in mathematics, is often regarded as a cube. This shape is based on six equal sides with the same length, breadth, and height. Now measure the length of the dice, suppose it measures 1 cm. Do the same for height and breadth as well.

We can see that both the height and breadth also measure 1 cm as all sides are equal for a square. Now, as I mentioned earlier, the formula will be applied which goes like; 

The volume of Square = L x B x H

Putting the values, we can conclude that the volume for this cube will be 1 cm3. Which can also be stated as the volume of cube/dice is a one-centimeter cube. Volume is always measured in centimeter cube or cm3; it is the unit of volume.

Units of volume and cubic feet

The volume for any object is expressed in terms of its unit. The most common unit used is centimeter cube or cm3 and meter cube or m3. But other units are also used to express the volume of various objects because of the requirement of that object or due to calculations.

Cubic feet are also known as the cubic foot, which is expressed as ft3 is a unit mostly used to express the volume of liquid holding containers or different water bodies. This is an imperial and US customary (non-metric) unit of volume. 

Cubic foot or feet is most commonly used in the United States and the United Kingdom. In mathematical terms, this unit can be defined as the volume of a cube with sides of one foot, which is 0.3048 m in length. Its volume is 28.3168 L, which is around one by 35th part of a cubic meter.

Volume of Cone

A cone is an object or a three-dimensional figure which has a circular base and a curved surface, around it, connects the base and the vertex. This curved surface tapers or decreases in size to a vertex at the top. The height of the cone is described as the perpendicular distance from the base to the vertex. 

There are two more types of cone present, which are known as Right cone and Oblique cone. The right cone has the vertex vertically above the center of the base, while the oblique has an irregular shape with the vertex not vertically present above the center of the base.

A formula is used to calculate the volume of the cone, which is stated as follows:

Ares of Cone = 13r2h

If you instantly want to calculate cone volume, here is the cone volume calculator

This formula can be interpreted as the volume of a cone is equal to one-third of the product of the area of the base and the height. And here r is the radius of the base and h is the perpendicular height of the cone.

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