NCERT Solutions for Class 9 Maths Exercise 11.2 Surface Areas and Volumes in Hindi and English Medium updated for CBSE Session 2023-24. Questions of ex. 11.2 of 9th Maths are revised as per the rationalised syllabus based on new NCERT books for CBSE 2023-24.
|Chapter: 11||Exercise: 11.2|
|Topic:||Surface Areas and Volumes|
|Content:||Text and Videos|
|Medium of Solution:||Hindi and English|
Class 9 Maths Exercise 11.2 Questions in Detail
- Find the surface area of a sphere of radius: (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm
- Find the surface area of a sphere of diameter: (i) 14 cm (ii) 21 cm (iii) 3.5 m
- Find the total surface area of a hemisphere of radius 10 cm.
- 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.
- A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹16 per 100 cm².
- Find the radius of a sphere whose surface area is 154 cm².
- The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.
- A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
- A right circular cylinder just encloses a sphere of radius r. Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in (i) and (ii).
Sphere and its Parts
As we have mentioned above a sphere is a 3-dimensional solid figure, this is made of all points in the space which lie at the equidistance known as Radius (r). This origin fixed point is called the Center of the sphere.
Once you have the radius, the formulae are usually pretty straightforward to remember. Just as with the circumference of the circle, you will need to use π values. Basically, you can round this infinite number to 3.14 or 22/7. If the questions given in NCERT Maths (https://ncert.nic.in/) Exercise 11.2 of class 9, if value of pi is not given, we can take it 22/7 or 3.14 as per our convenience.
Formulae for Surface Areas of Sphere
As per stated information you will get the following formulae for Curved Surface Area or Total Surface Area as 4πr². The figure 18, shown in Maths textbooks, is sphere. When we will cut it in half, get two equal parts of the sphere that is known hemisphere.
Similar to the above given formulae there are shall be four formulae that are related to the Sphere. You have to remember the Surface area of a sphere, the surface area of the hemisphere, curved surface area, and total surface area of hemisphere.
Solving process of Exercise 11.2 in Class 9 Maths
Most of the questions of Class 9 Maths Exercise 11.2 are based on direct formula. The best part of the formulae is that you can derive it to which will help you to remember for a longer time.
It is absolutely necessary to remember these formulae. This could be a little difficult to remember but it is the best way for solving surface area and volume. You can make your surface area concepts to learn and demonstrate to your friends how the concept actually works.
Surface areas in day to day life
For instance – use different shape containers such as bread, biscuits, and butter. Cut some of the edges so that they stay together, but can be unfolded to show how different surfaces make the shape and what measurements are.
These practical activities and manipulative are so effective that they shall help you then imagine the function of the shapes and surfaces. In 9th Maths NCERT Exercise 11.2 all the 9 questions are easy to solve. Most of the questions ask you to calculate the spheres-related areas.
Is exercise 11.2 of class 9 Maths NCERT textbook important for exam?
Chapter 11 surface areas and volumes of class 9 Maths NCERT textbook is considered as one of the important exercises. It covers basic concepts in geometry like area, perimeter, volume and surface area of different shapes. Exercise 11.2 of chapter 11 of 9th Mathematics covers questions focused on sphere and hemisphere geometric shapes.
What can help students to perform better in exercise 11.2 of grade 9 Maths?
To perform well in exercise 11.2 questions of class 9 Maths NCERT textbook, students should first understand the basics of mensuration along with the formulae given here. Now they feel easiness during the practice or solving various problems from the textbook. They should also take help of online resources like video tutorials, online practice tests and worksheets to strengthen their understanding of the concepts.
How to prepare exercise 11.2 of class 9 Maths to score well in CBSE exam?
To prepare the exercise 11.2 chapter 11 of class 9 Maths, students should once derive the formula related to this exercise. After derivation, they will be confident to form formula for any given combined figure. This chapter is important as it lays the foundation for higher level mensuration topics such as 3-dimensional geometry, coordinate geometry and calculus. So paying extra attention to formulae derivation and revision would enhance the performance in exercise 11.2 of class 9 Maths.