NCERT Exercise 13.3 Class 9 Maths Solutions - Embibe
• Written By Anjali Choudhury
• Written By Anjali Choudhury

# NCERT Solutions for Surface Areas and Volumes Exercise 13.3 Class 9 Maths NCERT Exercise 13.3 Class 9 Maths Solutions: Class 9 Maths chapter 13 exercise 13.3 NCERT solutions will help students understand ‘Surface Areas and Volumes’ in detail. NCERT solutions for exercise 13.3 Class 9 Maths are prepared and solved by subject experts at Embibe. These NCERT solutions will enhance the mathematical skills of the students and will help them gain an overview of the question paper pattern.

The NCERT exercise 13.3 Class 9 Maths solutions are explained in a step-by-step manner to help students understand the basic concepts of the chapter. Students will also learn complex problem-solving skills to ace the exams and use them in their higher studies. Embibe aims to assist students in confidently facing their exams and solving any question quickly. All the NCERT solutions are explained in detail and will help students understand the chapter’s concepts better. Read on to learn more.

## NCERT Exercise 13.3 Class 9 Maths Solutions: Overview

Students can practice and improve their Math skills by working through the NCERT exercise 13.3 Class 9 Maths solutions. As per the syllabus, these detailed solutions include questions from the exercises in the NCERT textbooks. The main goal of these questions is to help students do well on their first and second term exams in Class 9. Chapter 13 Surface Areas and Volumes NCERT solutions for Class 9 Maths ex 13.3 will help students gain experience in solving these in-text exercises. They will be better able to score well and confront exams with more confidence.

Before we jump into further details, let us have an overview of NCERT solutions for exercise 13.3 Class 9 Maths:

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### NCERT Exercise 13.3 Class 9 Maths Solutions: Free PDF

Our subject experts and experienced teaching faculty at Embibe have developed a complete collection of questions and NCERT solutions from the exercises and relevant explanations. NCERT solutions for Class 9 Maths chapter 13 exercise 13.3 are designed to assist students in achieving high marks in their first and second term exams. We provide good illustrations and explanations so that students can better understand the subject.

After going through the in-text exercise questions, students will learn more about the chapter and its formulas. Students will learn how to apply them and use them to derive the correct answers. Embibe provides free NCERT solutions PDF for students to help them with their exam preparations. Refer to the link below and download the NCERT solutions for ex 13.3 Class 9 Maths to study offline and ace the exams:

### About NCERT Exercise 13.3 Class 9 Maths Solutions

The NCERT solutions for Class 9 Maths chapter 13 exercise 13.3 ‘Surface Areas And Volumes’ introduce a three-dimensional depiction of the right circular cone using a simple activity involving a paper and a string. When you rotate a right-angled triangle with a string attached to one of the perpendicular sides, you get a right circular cone. It will be easy for the students to recognise it as an ice cream cone. For a student’s understanding, the formula for computing the curved surface area of the right circular cone is deduced step by step.

The NCERT solutions for Class 9 Maths chapter 13 exercise 13.3 comprises eight questions, seven of which are simple to solve and one of which may take some time to complete; the details of NCERT solutions for exercises 13.3 Class 9 Maths can be found in the pdf link provided above. The formulas used in NCERT exercise 13.3 Class 9 Maths solutions are listed below:

• Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl,
where ‘r’ is its base radius and ‘l’ its slant height
Then, ‘l’ = Square root of (r2 + h2)
• Total Surface Area of a Cone = πrl + πr 2 = πr(l + r)

### NCERT Exercise 13.3 Class 9 Maths Solutions: Chapter Summary

In our daily lives, we all witness a variety of objects. The students should be able to sketch the figures of these solid objects on plain paper as plane figures based on their prior understanding from previous classes. They will learn how to calculate the surface areas and volumes of cuboids, cylinders, cones, and spheres in the NCERT Solutions for Class 9 Maths Chapter 13 ‘Surface Areas and Volumes’ because these help in knowing how much space a solid occupies in space, which is very useful to know in our day to day lives.

These NCERT solutions for Class 9 Mathematics Chapter 13 – Surface Areas and Volumes – will assist students in adequately understanding this topic. The term ‘volume’ refers to the amount of space inside a hollow item or solid, whereas ‘surface area’ refers to the space occupied by the surface of anything. If one intends to fill a cuboid-shaped hollow container with water, the volume of the container can be calculated by measuring the length, breadth, and height of the container. These ideas are significant in a variety of concepts. Below we have mentioned the number of questions asked in each exercise from chapter 13:

• Class 9 Maths Chapter 13 Exercise 13.1 – 8 Questions
• Class 9 Maths Chapter 13 Exercise 13.2 – 11 Questions
• Class 9 Maths Chapter 13 Exercise 13.3 – 8 Questions
• Class 9 Maths Chapter 13 Exercise 13.4 – 9 Questions
• Class 9 Maths Chapter 13 Exercise 13.5 – 9 Questions
• Class 9 Maths Chapter 13 Exercise 13.6 – 8 Questions
• Class 9 Maths Chapter 13 Exercise 13.7 – 9 Questions
• Class 9 Maths Chapter 13 Exercise 13.8 – 10 Questions
• Class 9 Maths Chapter 13 Exercise 13.9 – 3 Questions

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### Important Questions From Surface Areas and Volumes

Some of the important questions from the chapter are mentioned below:

Q.1: The paint in a certain container is sufficient to paint an area equal to 9.375 sq.m. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

Q.2: The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of Rs.7.50 per sq.m.

Q.3: Curved surface area of a right circular cylinder is 4.4 sq.m. If the radius of the base of the cylinder is 0.7 m, find its height.

Q.4: In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

Q.5: The height of a cone is 16 cm and its base radius is 12 cm. Find the curved surface area and the total surface area of the cone. (Take π = 3.14)

Q.6: The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs.210 per 100 sq.m.

Q.7: The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.

Q.8: The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Q.9: A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

Q.10: Meera has a piece of canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it.

### Benefits of NCERT Exercise 13.3 Class 9 Maths Solutions

Some of the benefits of NCERT ex 13.3 Class 9 Maths solutions are mentioned below:

• The NCERT solutions are offered step-by-step to help students understand how to answer questions on the exam.
• The examination is based on the NCERT textbooks. To do well on the final exams, students must carefully go over the in-text exercises.
• Students develop complex problem-solving skills when studying from the NCERT textbooks. This helps them in obtaining excellent exam results.
• Students develop time management skills in preparation for exams because practising allows them to answer any question in a timely manner.
• The NCERT solutions assist students in comprehending the types of questions that will be asked throughout the exam. As a result, they can get good results on their final exams.

### FAQs on NCERT Exercise 13.3 Class 9 Maths Solutions

Some of the frequently asked questions on NCERT exercise 13.3 Class 9 Maths solutions are mentioned below:

Q.1: What important topics are covered in NCERT exercise 13.3 Class 9 Maths solutions?
Ans: The topic covered in NCERT exercise 13.3 Class 9 Maths solutions are surface area of a right circular cone.

Q.2: How many questions are there In chapter 13 of Class 9 Maths?
Ans: There are a total of 75 questions in chapter 13 of Class 9 Maths- Surface Areas and Volumes.

Q.3: Are the NCERT solutions for exercise 13.3 Class 9 Maths available on Embibe?
Ans: Yes, the NCERT solutions for exercise 13.3 Class 9 Maths are available on Embibe and are easily accessible.

Q.4: Are the NCERT solutions for Class 9 Maths chapter 13 exercise 13.3 available for free?
Ans: Yes, the NCERT solutions for Class 9 Maths chapter 13 exercise 13.3 are available for free on Embibe.

Q.5: What is the formula for the volume of a cone?
Ans: The formula for the volume of a cone is (1 / 3) πr²h.

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