Volume formulas for Cylinder | Derivation & Solved Examples, Check How to Calculate

Cylinder Volume Formula

cylinder-volume-formula

Students who are searching for the Cylinder Volume Formula and solved examples based on volume formulas for cylinder then you are at the right place. It is compulsory for the candidates who are going to appear in the exams that they should have the knowledge of Cylinder Volume Formula and also know the procedure how to calculate the big numbers in less time. In many competitive exams like SSC, UPSC, Bank PO etc. there is Quantitative Aptitude section. This section is fully based on Maths formulas, shortcut tricks and tips. This section requires 20 minutes but those aspirants who don’t have the knowledge about Cylinder Volume Formula could not be able to finish the section in a given time period.

For them we the team of resultinbox.com are providing some cylinder volume formulas and some solved illustrations for the convenience of all candidates. Keep on practicing the formulas and important topics daily so that you will achieve success. Make a time table so that you will complete your preparation before 10-15 days from exams dates.

Surface Area and Volume of a Cylinder

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How to find the Volume of a Cylinder

Although a cylinder is technically not a prism, it shares many of the properties of a prism. Like prisms, the volume is found by multiplying the area of one end of the cylinder (base) by its height.

Since the end (base) of a cylinder is a circle, the area of that circle is given by the formula:

Area= πr2

Multiplying by the height h we get

Volume= πr2h

Where:

π is Pi, approximately 3.142
r  is the radius of the circular end of the cylinder
h  height of the cylinder

Derivation

A cylinder is nothing but a set of circular discs stacked one upon the other. So if we compute the space occupied by each of these discs and add them up, what we get is the volume of the cylinder.

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Volume Formulas for Basic Shapes

Shapes Volume Formula Variables
Rectangular Solid or Cuboid l.w.h l = Length,
w = Width,
h = Height
Cube a3 a = length of edge or side
Cylinder πr2h r = radius of the circular edge,
h = height
Prism B. h B = area of base, (B = side2 or length.breadth)
h = height
Sphere 4/3 πr3 r = radius of sphere
Pyramid 1/3 B.h B = area of base,
h = height of pyramid
Right Circular Cone 1/3πr2h r = radius of the circular base,
h = height (base to tip)
Square or Rectangular Pyramid 1/3lwh l = length of base,
w = width of base,
h = height (base to tip)
Ellipsoid 4/3 πabc a, b, c = semi – axes of ellipsoid
Tetrahedron √2/12 a3 a = length of the edge

Cylinder Volume Formula

Solved Examples based on Cylinder Volume Formula

1) What is the volume of the cylinder with a radius of 2 and a height of 6?

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Solution: Volume =π*(r)2 (h)

Volume = π*(2)2 (6) = 24

2) What is the volume of the cylinder with a radius of 3 and a height of 5?

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Solution: Volume = π *(r)2 (h)

Volume = π *(3)2 (5) = 45 π

3) What is the area of the cylinder with a radius of 6 and a height of 7?

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Solution: Volume= π *(r)2 (h)

Volume = π *(6)2 (7)= 252 π

 4) The volume and height of a cylindrical container are 440 m3 and 35m respectively. Calculate its radius of the base.

Solution: Volume of the cylindrical container = 440 m³

Height of the cylindrical container = 35 m

Or 440 m³= πr2h

=> r² = 4m

=> r = 2 m

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The radius of the base of the cylindrical container is 2 m.

5) How many litres of water can a cylindrical water tank with base radius 20 cm and height 28 cm hold?

Solution: Base radius of the cylindrical water tank, r = 20 cm

Height of the cylindrical water tank, h = 28 cm

Volume of the cylindrical water tank = πr2h

1 cubic centimeter = 0.001 litre = litre

∴ 35200 cubic centimeter = 35.2 litres

The cylindrical water tank can hold 35.2 litres of water.

6) The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.

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Solution: The cross section of the pipe is a ring:
Area of ring = [π (2.4)2– π (2)2]= 1.76 π cm2

Volume of pipe = 1.76 π × 10 = 55.3 cm3
Volume of metal used = 55.3 cm3

7) Find the volume of a cylinder if its radius is of 4 cm and the height is of 5 cm.

Solution:  

The volume of the cylinder is

V= π r2 h= 3.14159 * 42 * 5 =3.14159*16*5 = 3.14159*80 = 251.33 cm

The volume of the cylinder is 251.33 cm2 (approximately).

8) Two cylinders are joined in a way that the base of one cylinder is overposed on the base of the other as shown in the  Figure 2a.
The radius of one cylinder is  10 cm  and the height is  4 cm.  The radius of the other cylinder is  4 cm  and the height is  10 cm.
Find the volume of the composite body.

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Solution:

The Figure 2b  represents the side view of the two cylinders.

The common axis is shown in blue in the Figures 2a  and  2b.

The volume under consideration is composed of the volume of the first

cylinder and the volume of the second cylinder:

V = π.r12 h1 + π.r22.h2 = π.102.4+ π.42.10= π (10.4+16.10)

= 560=560*3.14159=1759.29cm3

The volume of the composite body is 1759.29 cm3 (approximately).

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Note The assumption that the cylinders are co-axial is not necessary.  The result is valid for non-axial cylinders too.

9) Find the volume of the solid body concluded between two co-axial cylindrical surfaces  (Figure 3)  of the radii of  8 cm  and  4 cm  respectively if the common height of the two cylindrical shells is of  10 cm.

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Solution:

The Figure 3 represents the solid body concluded between two co-axial cylindrical

Surfaces.

Their common axis is shown in blue in this Figure.

The volume under consideration is the volume of the larger cylinder minus the volume

of the smaller one,  i.e

V = π.82.10 – π.42.10 = π. (64-16).10=3.14159*48*10=1507.96cm3 (approximately).

The volume of the solid body under consideration is 1507.96 cm%5E3 (approximately).

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10) Four through cylindrical holes are made in the solid cylinder parallel to its axis of symmetry (Figure 4).
Find the volume of the obtained solid body if the diameter of the original cylinder is 20 cm,  its height is  16 cm  and the diameter of each hole is  4 cm.

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Solution:  

The volume of the original solid cylinder is V= π.r2 h = π.*102 * 16 = 1600. π.

Hence the volume of the solid body under consideration is

V – 4.v Hole = 1600. π – 4.64. π = 1344. π = 4220.16 cm3 (approximately).

The volume of the solid body under consideration is 4220.16 cm3 (approximately).

11) A through cylindrical hole is made in a rectangular prism (rectangular box)  of dimensions  3x4x5 cm  along its axis of symmetry parallel to the shortest edge  (Figure 5).
Find the volume of the obtained solid body if the diameter of the hole is 2 cm.

Solution:  

The volume of the original rectangular prism is

V prism= 3. 4. 5=60 cm3

The volume of the cylindrical hole is

V Hole = π r 2 h = π * 12 * 3 = 3. π

Hence, the volume of the solid body under consideration is

V = V prism – V Hole = 60 – 3. π = 60-3.3.14=50.58 cm3

The volume of the solid body under consideration is 50.58 cm3 (approximately).

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12) A swimming pool has a cylindrical shape.  Find the volume of the pool if its diameter is of  40 ft  and the depth is of  8 ft.

Solution:  The volume of the swimming pool is equal to the volume of a cylinder with the radius of 20 ft   and the height of 8 ft, i.e.

V = π r 2 h = π* 20 2 * 8 = 3200 π

Answer.  The volume of diving pool is 10048 cubic ft (approximately).

13) Calculate Volume of cylinder if r = 4 inches and h = 8 inches

Solution:  

= pi × r2× h

= 3.14 × 42× 8

= 3.14 × 16 × 8

= 3.14 × 128

Volume of cylinder = 401.92 inches3

14) Calculate the Volume of cylinder if r = 2 cm and h = 5 cm

Solution:  

= pi × r2× h

= 3.14 × 22× 5

= 3.14 × 4 × 5

= 3.14 × 20

= 62.8 cm3

15) An oil storage tank has a cylindrical shape.  Find the volume of the storage tank if its diameter is of 60 m and the height is of 20 m.

Solution:  

V = π r 2 h = π*30 2 * 20 = 1800 π = 56520 m 3 (approximately).

Apply the formula for the volume of a cylinder.
The volume of the storage is equal to

The volume of diving pool is 56520 m3 (approximately).

Official Note

We like to say all the very best to the students who are going to be appear in the competitive exam. Aspirants don’t get confused among the formulas, read and understand it. Write the formulas in your notebook for practice and be confident at the time of examination.

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