**Cylinder Volume Formula**

Aspirants who are in quest of **Cylinder Volume Formula **can get the easy tricks and Formula of volume of cylinder from this page. With the help of the formulas and examples explained here, you can easily solve questions related to volume of cylinder. Mostly children face problem to solve the volume of the solid shapes like cone, cylinder, cuboid and others. So here we are providing you with some of the basic Cylinder Volume Formula. You must remember these formulas to solve the questions for volume of cylinder.

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**Cylinder Volume Formula**

Volume of cylinder is usually measured in terms of cubic units. Volume is the capacity of any container or object to hold the amount of liquid in it. You can use arithmetic formulas to find the volume of cylinder. The formula for volume of a cylinder is as follows:

__Formula for calculating volume of cylinder__:

A cylinder with radius r units and height h units has a volume of V cubic units given by

V= πr^{2}h

Or

The volume of the cylinder can be measured as = πr^{2}h, where r = d/2

- r = radius of the circular edge
- d = Diameter of the circular edge
- h = height of the cylinder

__Tricks to Solve Volume of Cylinder__:

**Example 1: **

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

Volume of cylinder = π × r^{2}× h

Volume of cylinder = 3.14 × 2^{2}× 5

Volume of cylinder = 3.14 × 4 × 5

Volume of cylinder = 3.14 × 20

Volume of cylinder = 62.8 cm^{3}

**Example 2: **

Calculate Volume cylinder if r = 4 inches and h = 8 inches

Volume of cylinder = pi × r^{2}× h

Volume of cylinder = 3.14 × 4^{2}× 8

Volume of cylinder = 3.14 × 16 × 8

Volume of cylinder = 3.14 × 128

Volume of cylinder = 401.92 inches^{3}

Get Here: __Maths Formulas PDF__

__Question and Answers based on cylinder volume formula__

Question 1) Find the surface area and volume. Answer with proper units like m2and m3.

To represent m2, use “sq m”, etc. To answer with π, use “pi”.

Sample area: 5π m2 becomes “5pi sq m”. Sample volume: 5π m3becomes “5pi cu m”.

Solution: The surface area of a cylinder is the area of the bottom and top circles and the area of the side of the cylinder. This can be expressed as follows:

SA = 2πrh + 2πr^{2}

SA = 2π × (3cm) × (2 cm) + 2π × (3 cm)^{2}

SA = 2π × (6 cm2) + 2π × (9 cm^{2})

SA = 12π cm2^{ }+ 18π cm^{2}

SA = 30π cm^{2}

The volume of a cylinder is the area of the base circle times the height of the cylinder.

V = bh = πr^{2}h

V = π × (3 cm)^{2 }× (2 cm)

V = π × (9 cm^{2}) × (2 cm)

V = π × (18 cm^{3})

V = 18π cm^{3}

Question 2) Farmer Jones owns a citrus tree farm in Florida. During some parts of the year the amount of rain in Florida is not sufficient to maintain maximum growth of citrus so farmer Jones is going to buy a water tank. Find how much water it will hold if it is a right circular cylinder with a height of 10 feet and a radius of radius of 5 feet.

Solution: By substitution,

V = r^{2}h

V = (5)^{2}(10)

V = (25)(10)

V = 250 ft^{3}

If we approximate the value of π = 3.14 then

V = 785 ft^{3}

Question 3) A soup can has a diameter of 10 cm and a height of 15 cm. What is the volume of the soup in the can if 0.5 cm of space is left at the top of the can to allow for expansion?

Solution:

Step 1: Find the area of the base.

The radius of the bottom of the can equals 5 cm since it is half of the diameter (10 cm).

By substitution,

B = r2

B = (5)2

B = (25)

B = 25 cm2

If we approximate the value of = 3.14 then

B = 78.5 cm2

Step 2: Find the height of the soup in the can.

The can is 15 cm tall but 0.5 cm of space is to be left at the top of the can to allow for expansion,

h = 15 cm – 0.5 cm = 14.5 cm

Step 3: Find the volume of soup.

By substitution,

V = Bh

V = (78.5)(14.5)

V = 1138.25 cm3

Check Out: __Compound Interest Formula –With Example__

Question 4) Find the surface area and volume. Answer with proper units like m^{2} and m^{3}.

To represent m^{2}, use “sq m”, etc. To answer with π, use “pi”.

Sample area: 5π m^{2} becomes “5pi sq m”. Sample volume: 5π m^{3} becomes “5pi cu m”.

Solution: The surface area of a cylinder is the area of the bottom and top circles and the area of the side of the cylinder. This can be expressed as follows:

SA = 2πrh + 2πr2

SA = 2π × (7yd) × (1 yd) + 2π × (7 yd^{)2}

SA = 2π × (7 yd^{2}) + 2π × (49 yd^{2})

SA = 14π yd^{2} + 98π yd^{2}

SA = 112π yd^{2}

The volume of a cylinder is the area of the base circle times the height of the cylinder.

V = bh = πr^{2}h

V = π × (7 yd)^{2} × (1 yd)

V = π × (49 yd^{2}) × (1 yd)

V = π × (49 yd^{3})

V = 49π yd^{3}

Question 5) Calculate the volume of a cylinder having height 20 cm and base radius of 14 cm. (Take π= 22/7)

Solution: Volume of a cylinder = πr^{2}h

=> 227×14×14×20 = 12320 cm3

Question 6) Calculate the radius of base of a cylindrical container of volume 440 cm3. Height of the cylindrical container is 35 cm. (Take 𝝿 = 22/7)

Solution: Volume of a cylinder = (area of base) × height of cylinder

Area of base = (Volume of cylinder)/ (height of cylinder) = 440/35cm2

=> 227×r2= 440/35

=> r2 = 4

=> r = 2 cm

Do You Know: __How to Prepare For Maths__

Question 7) 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.

Solution: The cross section of the pipe is a ring:

Area of ring = [π (2.4)^{2}– π (2)^{2}]= 1.76 π cm^{2}

Volume of pipe = 1.76 π × 10 = 55.3 cm^{3 }

Volume of metal used = 55.3 cm^{3}

Question 8) Find the volume of cylinder with base area = 50 cm^{2}, h = 7 cm

Solution: 350 cm^{3}

Question 9) Find the volume of cylinder with diameter = 28 cm, h = 5 cm

Solution: 3077 cm^{3}

Question 10) Find the volume of cylinder with r = 5 cm, h = 12 cm

Solution: 942 cm^{3}

Check Out: __Best Institutes for Mathematics__

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