NCERT Solutions for Class 9 Maths Chapter 13: NCERT Solutions for Chapter ‘Surface Area and Volume’ is a valuable resource to help students score well in exams and other competitive exams. In this article, we have provided a detailed solution to the questions of the NCERT Class 9 Maths Chapter 13. Class 9 Maths Chapter 13 NCERT solutions are designed based on the latest CBSE syllabus and exam pattern guidelines.
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NCERT Solutions for Class 9 Maths Chapter 13
In NCERT Class 9 Maths Chapter 13, students will learn about the surface areas and volumes of different shapes, such as cuboids, cubes, cylinders, and spheres. The topics are tabulated below:
Surface Areas of a Cuboid and a Cube
Surface Area of a Right Circular Cylinder
Surface Area of a Right Circular Cone
Surface Area of a Sphere
The volume of a Cuboid
Volume of a Cylinder
Volume of a Right Circular Cone
Volume of a Sphere
Practice CBSE Class 9 Mathematics Questions with Hints & Solutions Here!
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How to Prepare for CBSE Class 9 Maths Surface Areas and Volumes?
Students must observe the number of solid shapes to calculate different shapes’ surface area and volumes. When we measure the surface area and volume of the solid shapes, we consider all three dimensions: length, breadth, and height. Therefore, students need to have a proper understanding of shapes and structures. When composite shapes’ surface area and volume are calculated, the shapes are broken into different constituting shapes. This calculation process is similar to breaking a bigger problem into smaller problems, to reach an accurate solution.
Some of the important questions from this chapter are as follows:
1 Mark Important Questions fromSurface Areas and Volumes
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
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?
The 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.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
2 Mark Important Questions fromSurface Areas and Volumes
Three cubes each of sides 5 cm are joined end to end. Find the surface area of the resulting cuboid.
In a hot water heating system, there is cylindrical piping of length 28m and diameter 5 cm. Find the total radiating surface in the system.
A joker’s cap is in the form of a circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
3 Mark Important Questions fromSurface Areas and Volumes
A rectangular water tank of base 11 m × 6 m contains water up to a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m by 15 m by 6 m. For how many days will the water of this tank last?
4 Mark Important Questions fromSurface Areas and Volumes
In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 97280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.
A container opened from the top and made up of a metal sheet, in in the form of a frustum of a cone height 16 cm with radii of its lower and upper ends as 8 cm and 20 am respectively. Find the cost of milk, which can fill the container completely at the rate of Rs 20/litre. Also, find the cost of metal sheet used to make the container, if it costs Rs 8/100 cm2.
CBSE Class 9 Maths Chapter 13: Summary
Surface Areas and Volumes explains the relationship between the length and breadth of a figure. For example, a cuboid is formed by six different rectangles. So, if students want to find the surface area of the cuboid, then they need to find the area of all the rectangles. After finding the areas of all the surfaces, they need to add them, which will give them the surface area of the cuboid.
Similarly, students can also find out the surface area of the cylinder. This chapter is filled with solved examples and exercises. Students must know the correct formulas and how to apply them. Thus, practicing the questions is the best way to master this chapter.
Surface Area is the area of the outer part of any 3D figure, and Volume is the capacity of the figure, i.e. the space inside the solid. Surface Areas and Volumes is one of the most important chapters of CBSE Class 9 Maths as it builds a strong foundation for higher classes as well as for competitive exams like Olympiads.
NCERT Class 9 Maths Chapter 13: Important Formulas
We have listed the most important and basic formulas in this chapter. Students should take a print out of this page or note them down to revise them everyday. Regular practice is the best way to remember formulas in Surface Area and Volume. Only then students can recall the formula correctly and apply it at the appropriate place. The formulas as mentioned in NCERT Class 9 Maths Chapter 13 are as follows:
1. Surface area of a cuboid = 2 (lb + bh + hl) 2. Surface area of a cube = 6a² 3. Curved surface area of a cylinder = 2πrh 4. Total surface area of a cylinder = 2πr(r + h) 5. Curved surface area of a cone = πrl 6. Total surface area of a right circular cone = πrl + πr² , i.e., πr (l + r) 7. Surface area of a sphere of radius r = 4πr² 8. Curved surface area of a hemisphere = 2πr² 9. Total surface area of a hemisphere = 3πr² 10. Volume of a cuboid = l × b × h 11. Volume of a cube = a³ 12. Volume of a cylinder = πr²h 13. Volume of a cone = (1 / 3) πr²h 14. Volume of a sphere of radius r = (4/3) πr³ 15. Volume of a hemisphere = (2 / 3) πr³ [Here, letters l, b, h, a, r, etc. have been used in their usual meaning, depending on the context.]
FAQs on NCERT Solutions for Class 9 Maths Chapter 13
Q.1. What is the Surface Area and Volume? Ans. Surface Area is the area of the outer part of any 3D figure, and Volume is the capacity of the figure, i.e. the space inside the solid.
Q.2. How can I find out the surface area of Cuboid? Ans. If you want to find the surface area of the cuboid, then you need to find the area of all the rectangles. After finding the areas of all the surfaces, you need to add them, which will give you the surface area of the cuboid.
Q.3. Why should I opt for NCERT Solutions for Class 9 Maths Chapter 13 by Embibe? Ans. The concepts are explained in simple language in the NCERT Solutions for Class 9 Chapter 13 by Embibe. A team of experts prepares the NCERT Solutions at Embibe with the goal of helping students enhance their exam preparation. It will also help you in finishing your homework. Moreover, if you can solve the NCERT in-text questions and exercises, you will be able to score better marks in the final examination.
Q.4. How many exercises are involved in Class 9 Maths Chapter 13? Ans. There are 9 exercises in Class 9 Maths Chapter 13. The list of questions in each one are as follows:
Q.5. Are the NCERT Solutions for Class 9 Maths Chapter 13 easy to understand? Ans. NCERT Solutions for Class 9 Maths Chapter 13 by Embibe will help you in understanding the chapter better. The solutions have been explained in a step-by-step manner so that any class 9 student can understand the topic well.