NCERT Solutions for Exercise 8.4 Class 10 Maths Trigonometry

March 28, 202339 Insightful Publications

**Volume of Cylinder: **A cylinder is a three-dimensional structure considered to be one of the most important geometrical shapes. The shape of the cylinder looks like tin or a can and has two parallel circular bases. The distance between the two circular bases is called the height of the cylinder. The circular base has a radius of r and the cylinder has a height of h. Students learn the concepts of surface areas and volume of cylinder at an early age in order to solve mathematical calculations.

Since the cylinder is three-dimensional, it has surface area and volume. Here, the volume is the space occupied by the cylinder. Students preparing for competitive exams must have thorough knowledge about the concept in order to fetch more marks in this particular topic. Also, check **NCERT Solutions for Class 9 Maths Chapter 13** for better understanding of the surface areas and volumes of geometrical structures. We will provide detailed information on the volume of cylinder in this article. Read on to find out about its definition, formula, properties, and few solved examples.

A cylinder is a three-dimensional structure that is held by a curved surface at a fixed distance. The line segment joining the two centers of the circular bases is called the height of the cylinder. The cylinder has two bases that are circular in shape and are parallel to each other. Examples of cylinders are cans, tins, pipes, gas cylinders etc.

The volume of cylinder is described as the space occupied by the cylinder.

**Check** – **Volume of Hemisphere**

The properties of cylinders are as follows:

- The bases of the cylinder are parallel to each other.
- Cylinders with circular bases are called right circular cylinders.
- Similarly, cylinders with elliptical bases are called elliptical cylinders.

Download NCERT Solutions for Class 9 Surface Areas and Volumes |

We can calculate the volume of cylinder by using the formula below:

Volume of Cylinder= πr^{2}h cubic units |

Where r is the radius and h is the height of the cylinder

Check out the following solved examples on volume of cylinder:

** Example 1:** If the lateral surface of a cylinder is 94.2 cm^{2} and its height is 5 cm, then find (i) radius of its base (ii) its volume. (Use π = 3.14)

**Solution:** (i) Given, height (h) of cylinder = 5 cm

Let radius of cylinder be r.

CSA of cylinder = 94.2 cm^{2}

Hence, 2πrh = 94.2 cm^{2} ⇒ (2 × 3.14 × r × 5) = 94.2 ⇒ r = 3 cm

Volume of cylinder = πr2h = (3.14 × (3)2 × 5) cm^{3} = 141.3 cm^{3}

**Example 2: ** Assume π = 22/ 7, unless stated otherwise. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

** Solution:** Given, diameter of the cylindrical bowl = 7 cm Hence, radius of the cylindrical bowl = 7 2 = 3.5 cm

Height of the cylindrical bowl = 4cm

Volume of the cylindrical bowl = πr^{2}h

= 22 7 × (3.5)2 × 4 = (11 × 3.5 × 4)cm^{3}

= 154 cm^{3}

The amount of soup the hospital has to prepare daily for 1 patient = 154 cm^{3}

Hence, the amount of soup to be prepared for 250 patients = 154 × 250 = 38500 cm^{3}

= 38.5 litres (1 cm^{3} = 0.001 litres)

The frequently asked questions on volume of cylinder are given below:

Q. What is a cylinder?A. A cylinder is a three-dimensional structure that has two circular bases separated by a distance. |

Q. What are the examples of cylinder?A. The examples of the cylinder are tins, cans, gas cylinder, etc. |

Q. What is the volume of cylinder?A. The volume of cylinder is the space occupied by the cylinder in a three-dimensional space. |

Q. What is the formula of volume of cylinder?A. The formula of volume of cylinder is as follows: Volume of the Cylinder, V = πr ^{2}h cubic units Where r is the radius and h is the height |

We hope this article on volume of cylinder was helpful. Understanding the volume and surface area of geometrical structures will help you in solving mathematical problems in a fraction of seconds.

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