# NCERT Solutions for Class 10 Maths Chapter 13

NCERT Solutions for class 10 Maths Chapter 13 Surface areas and volumes all exercises (Ex. 13.1 to Ex. 13.5) for all boards. We have updated all the contents for new academic session 2021-2022. UP Board students are now using NCERT Textbooks for their course and exams, so they can download UP Board Solutions for Class 10 Maths Chapter 13 all exercises from the links given below. Contents are applicable for UP Board 2021-22 and CBSE Board in Hindi and English medium. Contents are free in PDF format to download without any login or registration. Download NCERT Solutions Online and Offline Apps for session 2021-2022 based on updated NCERT Solutions and latest NCERT Books 2021-22.

Previous year CBSE Exam question, important questions for practice are also given below. Download and practice to score good marks and solve your doubts easily.

## NCERT Solutions for class 10 Maths Chapter 13

• ### 10th Maths Chapter 13 Exercise 13.5

 Class: 10 Maths (English and Hindi Medium) Chapter 13: Surface areas and volumes

### 10th Maths Chapter 13 Solutions

CBSE NCERT Solutions for class 10 Maths Chapter 13 Surface areas and volumes exercises 13.1 to 13.5 are given here to free download in PDF or view online without downloading. All the solutions are updated for new academic session 2021-22 for UP Board, MP Board, Gujrat, CBSE board, etc., who are using latest NCERT Books for course.

#### Class 10 Maths Chapter 13 Exercise 13.1 Solution in Videos

Class 10 Maths Exercise 13.1 Explanation and Solution
Class 10 Maths Chapter 13 Exercise 13.1 Solution

#### Class 10 Maths Chapter 13 Exercise 13.2 Solution in Videos

Class 10 Maths Exercise 13.2 Explanation and Solution
Class 10 Maths Chapter 13 Exercise 13.2 Solution

#### Class 10 Maths Chapter 13 Exercise 13.3 Solution in Videos

Class 10 Maths Exercise 13.3 Explanation and Solution
Class 10 Maths Chapter 13 Exercise 13.3 Solution

#### Class 10 Maths Chapter 13 Exercise 13.4 Solution in Videos

Class 10 Maths Exercise 13.4 Explanation and Solution
Class 10 Maths Chapter 13 Exercise 13.4 Solution

#### Class 10 Maths Chapter 13 Exercise 13.5 Solution in Videos

Class 10 Maths Exercise 13.5 Explanation and Solution
Class 10 Maths Chapter 13 Exercise 13.5 Solution

### NCERT Solutions for Class 10 Maths Chapter 13

• NCERT Solutions 10th MathsExercise 13.1Read more
• NCERT Solutions 10th MathsExercise 13.2Read more
• NCERT Solutions 10th MathsExercise 13.3Read more
• NCERT Solutions 10th MathsExercise 13.4Read more
• NCERT Solutions 10th MathsExercise 13.5Read more

#### Previous Years Questions

ONE MARK QUESTIONS
1. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere? [CBSE 2017]
THREE MARKS QUESTIONS
1. A metallic solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made? [CBSE 2017]
FOUR MARKS QUESTIONS
1. In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If the tank is filled completely then what will be the height of standing water used for irrigation the park. Write your views on recycling of water. [CBSE 2017]
2. The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is 1/27 of the given cone, then at what height it is cut from its base? [CBSE 2017]
3. The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts. [CBSE 2017]

##### Objective of Surface areas and volumes

1. To identify situations where there is a need of finding surface area and where there is a need of finding volume of a solid figure and to find the surface areas & volumes of cuboids, cubes, cylinders, cones spheres and hemispheres, using their respective formulae. To solve some problems related to daily life situations involving surface areas and volumes of above solid figures.
2. In this chapter, we will deal with problems such as finding the area of sheet to covers a solid body, area of an object which is combination of two objects, finding the number of one object, required for creating another different object, finding the cost of ploughing a given field at a given rate, finding the cost of constructing a water tank with a particular capacity, finding area & volume of frustum (Frustum is a Latin word meaning ‘piece cut off’ and its plural form is ‘Frusta’) and the conversion of one solid into another solid on the basis of volume and so on.
For solving above type of problems, we need to find the perimeters and areas of simple closed plane figures (figure which lie in a plane) and surface areas and volumes of solid figures (figures which do not lie wholly in a plane). You are already familiar with the concepts of perimeters, areas, surface areas and volumes. In this chapter, we will study these in details.

###### Historical Facts!

Archimedes of Syracuse, Sicily, is remembered as the greatest Greek mathematician of the ancient era. He contributed significantly in geometry regarding the areas of plane figures and the areas and volumes of solid figures. He proved that the volume of a sphere is equal to two-third the volume of a circumscribed cylinder. ##### What are the topics to study in chapter 13 Surface Areas and Volumes of 10th Maths?

In chapter 13, Surface Areas and Volumes of class 10 math, students will study

1. Surface Area of a Combination of Solids.
2. Volume of a Combination of Solids.
3. Conversion of Solid from one shape to another.
4. Frustum of a cone.
5. Volume of the frustum of the cone.
6. Curved surface area of the frustum of the cone.
7. Total surface area of the frustum of the cone.
##### Which topics students should revise before starting chapter 13 of class 10 Maths?

Before starting chapter 13 of class 10 Maths, Students should revise all the formulas mentioned in chapter 13 (surface areas and volumes) of class 9th Maths.

##### Is there any optional exercise in chapter 13 of class 10th Maths?

Yes, there is an optional exercise in chapter 13 of class 10th maths. The fifth exercise (exercise 13.5) is the optional exercise of chapter 13 and is a challenging exercise. Exercise 13.5 is challenging because this exercise contains logical questions which require higher-order thinking skills. Students find this exercise a little complex as compared to other exercises of this chapter.

##### Is chapter 13 of class 10th math difficult to solve?

Chapter 13 of class 10th maths is not easy and not difficult. It lies in the middle of easy and difficult because some examples and questions of this chapter are easy, and some are difficult. However, the difficulty level of anything varies from student to student. So, Chapter 13 of class 10th maths is easy or not depends on students also. Some students find it difficult, some find it easy, and some find it in the middle of easy and difficult.               