Cylinder Volume

Different figures exist in geometry based on dimensions. In two-dimensional figures, triangles, squares etc., we can get only the area of these figures as there is no volume because there is no height or the third dimension.

However, in the case of three-dimensional shapes such as the sphere, cube, cylinder, and so on, each form has its surface area and volume.

Surface area is the area covered by the surface of a geometric shape or, in general, any object. On the other hand, volume is the capacity that the shape can hold or the space it occupies.

And below, we will discuss the volume of a cylinder, which is very widely used.

Cylinder

A cylinder is the most widely seen geometric 3D shape. We all have seen cylinders in many of our everyday objects, such as fuel containers, toilet paper, coffee mugs. This shape-cylinder comes from the word ‘kulindros.’ The word ‘kulindros’ means tumbler, a utensil in a cylindrical shape.

 A cylinder is a closed solid object with two parallel bases that are often round in shape and two parallel sides that join them. A curved column with circular bases can also be characterised as a cylinder. The cylinder is made up of two circles and one rectangle.

If we talk about the right circular cylinder, the bases or the circular disk are always congruent and parallel. This means the radius is always fixed and the same for both the disks.

If we look at the structure of the cylinder, we get two disks and a rectangle if we unroll the cylinder. The cylinder’s axis is the line that runs through the centre of the two circular bases.

Height (h) is the perpendicular distance between the two bases, as shown in the diagram. A radius is assigned to each base. The radius of the cylinder, denoted by “r,” is the distance between the centre and the outer limit of the two circular bases. 

The cylinder’s surface area and volume can be calculated using the height and radius measurements.

A Cylinder’s Volume

Suppose we have to determine how much of anything – any material or subject – fluid or solid can be stored in a cylinder. In that case, we have to calculate the density, the volume of the cylinder. In other words, we’re trying to figure out how big this box is. The volume of the cylinder involved determines the capacity of a cylindrical box. As a result, the volume of a three-dimensional shape equals the amount of space it takes up.

 The volume of a cylinder indicates the quantity of material it can carry or how much of any material can be immersed in it. The volume of a cylinder is calculated using the formula πr^2h, where r is the radius of the circular base and h is the cylinder’s height.

Volume of Hollow Cylinder

We measure two radiuses in the case of a hollow cylinder, one for the inner circle and one for the outer circle produced by the hollow cylinder’s base. If the two radii of the provided hollow cylinder are r1 and r2, and the height is ‘h,’ then the volume of the hollow cylinder can be represented as V = πh(r1^2– r2^2).

A cylinder can be constructed with two circular bases and a curved column. To calculate this curved column’s volume- a rectangle – we take the 3 D form of a rectangle. Yes, that is a cuboid. 

The volume of a cuboid is what we get by multiplying the rectangle’s area and its height; lb h. Similarly, in the case of a cylinder, we have to multiply the areas by the height. The area to be taken here is the area of circular bases or disks and the height of the column of the cylinder. This gives the resultant πr^2 h. Therefore,

The Volume of cylinder  = πr^2h

Example

1.Find the volume of a right circular cylinder with a radius of 6 cm and a height of 10 cm round to the nearest cubic centimetre.

Solution

The formula for the volume of a cylinder is V=Bh or V= πr^2h

The radius of the cylinder is 6 cm, and the height is 10 cm.

Substitute 6 for r and 10 for h in the formula V= πr^2h

V=π(6)^2(10)

 On simplification 

V=π(36)(10)

Therefore, the volume of the cylinder is about cubic centimetres.

Conclusion

We hope this answers your questions and dispels any doubts you may have regarding this extensively used geometrical symbol. To test your understanding and applicability, try these mathematics problems and exercises on the topic of  volume of cylinders and volume of hollow cylinder