NCERT Solutions for Class 9 Maths Chapter 11 Exercise 11.4 Surface Areas and Volumes in Hindi and English medium updated for academic session 2023-24. Question answers of ex. 11.4 class 9th Maths are revised according to rationalised syllabus and new NCERT books for CBSE 2023-24.
|Chapter: 11||Exercise: 11.4|
|Chapter Name:||Surface Areas and Volumes|
|Content Type:||Online Text Solution and Videos|
|Medium:||Hindi and English Medium|
Class 9 Maths Exercise 11.4 Questions in Detail
- Find the volume of a sphere whose radius is (i) 7 cm (ii) 0.63 m.
- Find the amount of water displaced by a solid spherical ball of diameter (i) 28 cm (ii) 0.21 m.
- The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm³?
- The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
- How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
- A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
- Find the volume of a sphere whose surface area is 154 cm².
- A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹4989.60. If the cost of white-washing is ₹20 per square metre, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome.
- Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the (i) radius r′ of the new sphere, (ii) ratio of S and S′.
- A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?
NCERT Solutions for Class 9 Maths Exercise 11.4
9th Maths Exercise 11.4 solutions is updated for CBSE and State board students as per new NCERT Book. Get the solutions in PDF and Videos format to download for offline use. Answers and solutions are simplified in such a way that student can understand easily.
Volume of a Sphere in Exercise 11.4
So far, we know that just like the circle which a two-dimensional figure is, a sphere is a 3-dimensional object. Every aspect of the object sphere can be defined mathematically. Till now we have understood how to calculate the curved surface area of sphere.
Now we will study to calculate the volume of the sphere. Since all the 3-dimensional objects consist of the one major factor that they occupies space means have volume. In class 9 Maths exercise 11.4, we will practice the different ways to calculate volume of sphere.
Ways to find the Volume of Sphere in Exercise 11.4
The volume of the object is to have the space to carry any substance inside. In the matter like sphere and hemisphere, the number of cubic units are that will fill a hollow thin sphere.
The hollow thin structure storage of the sphere or hemisphere is known as the volume of the Sphere or hemisphere. In 9th Mathematics Exercise 11.4, questions are based on volumes of sphere and hemi-sphere. Using just the value of radius or diameter, we can easily find it. To get to the answer we can take radius value into account that a sphere has.
Solutions of Exercise 11.4 in Class 9 Maths
The formula for volume of a sphere is 4/3 πr³. If radius or diameter of sphere is given, use the direct formula to find the volume of sphere. In some questions, the surface area of the sphere is given and we have to find the volume. In that case, find the radius first, using formula of surface area and then use this value of radius in formula of finding volume.
Volume of a Hemi-sphere
Since we have already learn the formula of Sphere, now it is easy to find its volume. This makes the explanation of hemisphere exponentially short which gives the formula 2/3 πr3.
This is because we know the hemisphere is the half of the full sphere. This is the logical answer of why the formula looks like that. Here is the thing to know the volume of a sphere is measured in cubic units. i.e. m³ and cm³. Class 9 Maths Ex. 11.4 NCERT Solutions (https://ncert.nic.in/) are given here in simplified format with complete explanation.
How many questions are there in exercise 11.4 of class 9 Maths?
In chapter 11 exercise 11.4 of class 9 mathematics, NCERT solutions have 10 questions of mensuration. These questions mainly ask you to use the formulae of volume in some way or another. Questions are easy to solve, just require to implement the right formula. Practicing questions with the help of the 9th Maths solution would make the concepts must easier to understand.
How to prepare the exercise 11.4 of 9th Maths for the exam?
To prepare for exercise 11.4 of class 9 Maths for the examination, students should first read and understand the formulae of the volume. It will help enough to solve the equations. They can practice solving as many questions related to exercise 11.4 as possible. The extra questions based on ex. 11.4 are also given here for practice. Additionally, students should use visual aids such as diagrams, charts, pictures, and explanation videos to help them better understand the concepts step by step.
Which is the most important question of 9th Maths exercise 11.4?
As we know that there are only 10 questions in exercise 11.4 of class 9 Maths. All of these are based on Volume formulae. We should practice questions 1, 2, 5, 8, and 9 as these are unique ones which can cover the entire exercise. If you practice these questions then you will cover most of the volume questions. In exercise 11.4 of 9th Maths, question 9 and 10 are considered as an important one.