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NCERT Solutions for Exercise 13.1 Class 10 Maths Chapter 13 - Surface Area and Volumes

NCERT Solutions for Exercise 13.1 Class 10 Maths Chapter 13 - Surface Area and Volumes

Edited By Ramraj Saini | Updated on Nov 27, 2023 05:35 PM IST | #CBSE Class 10th

NCERT Solutions For Class 10 Maths Chapter 13 Exercise 13.1

NCERT Solutions for Exercise 13.1 Class 10 Maths Chapter 13 Surface Area and Volumes are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 Maths ex 13.1 presents us with the surface area of combination of Solids. Some solids, such as the cuboid, cone, cylinder, and sphere, are recognisable to you from Class IX. You've also learned how to calculate their volumes and surface areas. In our daily lives, we come across a variety of solids that are made up of two or more of the fundamental solids.

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  1. NCERT Solutions For Class 10 Maths Chapter 13 Exercise 13.1
  2. Download Free Pdf of NCERT Solutions for Class 10 Maths chapter 13 exercise 13.1
  3. Assess NCERT Solutions for Class 10 Maths chapter 13 exercise 13.1
  4. Some More Information About NCERT Solutions for Class 10 Maths Exercise 13.1
  5. Benefits of NCERT Solutions for Class 10 Maths Exercise 13.1
  6. Key Features For Class 10 Maths Chapter 13 Exercise 13.1
  7. NCERT Solutions Subject Wise
NCERT Solutions for Exercise 13.1 Class 10 Maths Chapter 13 - Surface Area and Volumes
NCERT Solutions for Exercise 13.1 Class 10 Maths Chapter 13 - Surface Area and Volumes

In exercise 13.1 Class 10 Maths we have to find the surface area of the combined solids .Some of these solids are cylinders with both sides hemisphere , cone with hemisphere on top. Surface area can be categorized into two types of surface areas, the curved surface area and total surface area. 10th class Maths exercise 13.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

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Surface Areas and Volumes Class 10 Maths Chapter 13 Exercise: 13.1

Q1 2 cubes each of volume 64 cm 3 are joined end to end. Find the surface area of the resulting cuboid.

Answer:

We are given that volume of the cube =\ 64\ cm^3

Also, the volume of a cube is given by =\ a^3 ( here a is the edge of the cube)

Thus : a^3\ =\ 64

a\ =\ 4\ cm

Now according to the question we have combined the two cubes that edge lengths of the formed cuboid are 4 cm, 4 cm, and 8 cm.

The surface area of a cuboid is : =\ 2\left ( lb\ +\ bh\ +\ hl \right )

or =\ 2\left ( 8\times 4\ +4\times 4\ +\ 4\times 8 \right )

or =\ 2\left ( 80 \right )

or =\ 160\ cm^2

Thus the area of the formed cuboid is 160 cm 2 .

Q2 A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Answer:

Since the vessel consists of hemisphere and cylinder, thus its area is given by :

Area of vessel = Inner area of the cylinder(curved) + Inner area of hemisphere

The inner surface area of the hemisphere is :

=\ 2\pi r^2

or =\ 2\times \left ( \frac{22}{7} \right ) \times 7^2

or =\ 308\ cm^2

And the surface area of the cylinder is :

=\ 2\pi rh

or =\ 2\times \frac{22}{7}\times 7\times 6

or =\ 264\ cm^2

Thus the inner surface area of the vessel is = 308 + 264 = 572 \:cm^2.

Q3 A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer:

The required surface area of the toy is given by :

Area of toy = Surface area of hemisphere + Surface area of the cone

Firstly consider the hemisphere :

The surface area of a hemisphere is =\ 2 \pi r^2

or =\ 2 \times \frac{22}{7}\times \left ( 3.5 \right )^2

or =\ 77\ cm^2

Now for cone we have :

The surface area of a cone =\ \pi rl

Thus we need to calculate the slant of the cone.

We know that :

l^2\ =\ h^2\ +\ r^2

or =\ 12^2\ +\ 3.5^2

or =\ \frac{625}{4}

or l\ =\ \frac{25}{2}\ =\ 12.5\ cm

Thus surface area of a cone =\ \pi rl

or =\ \frac{22}{7}\times 3.5\times 12.5

or =\ 137.5\ cm^2

Hence the total surface area of toy = =\ 77\ +\ 137.5\ =\ 214.5\ cm^2

Q4 A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Answer:

It is given that the hemisphere is mounted on the cuboid, thus the hemisphere can take on complete as its diameter (which is maximum).

Thus the greatest diameter of the hemisphere is 7 cm.

Now, the total surface area of solid = Surface area of cube + Surface area of the hemisphere - Area of the base of a hemisphere (as this is counted on one side of the cube)

The surface area of the cube is :

=\ 6a^3

=\ 6\times 7^3\ =\ 294\ cm^2

Now the area of a hemisphere is

=\ 2\pi r^2

=\ 2\times \frac{22}{7}\times \left ( \frac{7}{2} \right )^2\ =\ 77\ cm^2

And the area of the base of a hemisphere is

=\ \pi r^2\ =\ \frac{22}{7}\times \left ( \frac{7}{2} \right )^2\ =\ 38.5\ cm^2

Hence the surface area of solid is = 294 + 77 - 38.5 = 332.5 \:cm^2 .

Q5 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.

Answer:

It is given that the diameter of the hemisphere is equal to the edge length of the cube.

The total surface area of solid is given by :

The surface area of solid = Surface area of cube + Surface area of the hemisphere - Area of the base of the hemisphere

The surface area of the cube =\ 6l^2

And surface area of the hemisphere:

=\ 2\pi r^2\ =\ 2\pi \left ( \frac{l}{2} \right )^2

Area of base of the hemisphere:

=\ \pi r^2\ =\ \pi \left ( \frac{l}{2} \right )^2

Thus the area of solid is:

=\ 6l^2\ +\ \pi \left ( \frac{l}{2} \right )^2\ unit^2

Q6 A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig.). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

1636091994484

Answer:

It is clear from the figure that the capsule has hemisphere and cylinder structure.

The surface area of capsule = 2 (Area of the hemisphere) + Area of the cylindrical part

Area of hemisphere =\ 2\pi r^2

or =\ 2\pi\times \left ( \frac{5}{2} \right )^2

or =\ \frac{25}{2} \pi\ mm^2

And the area of the cylinder =\ 2\pi rh

or =\ 2\pi \times \frac{5}{2}\times 9

or =\ 45 \pi\ mm^2

Thus the area of the solid is :

=\ 2\left ( \frac{25}{2} \right )\pi\ +\ 45 \pi

=\ 25\pi\ +\ 45 \pi

=\ 70 \pi

=\ 220\ mm^2

Q7 A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m 2 . (Note that the base of the tent will not be covered with canvas.)

Answer:

The canvas will cover the cylindrical part as well as the conical part.

So, the area of canvas = Area of cylindrical part (curved) + Area of the conical part

Now, the area of the cylindrical part is =\ 2\pi rh

or =\ 2\pi \times 2\times 2.1

or =\ 8.4 \pi\ m^2

And the area of the cone is =\ \pi rl

or =\ \pi \times 2\times 2.8

or =\ 5.6\pi\ m^2

Thus, the area of the canvas =\ 8.4\pi\ +\ 5.6\pi

or =\ 14\pi\ =\ 44\ m^2

Further, it is given that the rate of canvas per m 2 is = Rs. 500.

Thus the required money is =\ 500\times 44\ =\ Rs.\ 22,000

Q8 From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm 2 .

Answer:

Firstly we need to calculate the slant height of the cone :

l^2\ =\ r^2\ +\ h^2

or =\ (0.7)^2\ +\ (2.4)^2

or l^2\ =\ 6.25

or l\ =\ 2.5\ cm

Now, the total surface area of solid can be calculated as :

The surface area of solid = Surface area of cylinder + Surface area of cone + Area of base of the cylinder

The surface area of the cylinder is =\ 2 \pi rh

or =\ 2 \pi \times 0.7\times 2.4

or =\ 10.56\ cm^2

Now, the surface area of a cone =\ \pi rl

or =\ \pi \times 0.7\times 2.5

or =\ 5.50\ cm^2

And the area of the base of the cylinder is =\ \pi r^2

or =\ \pi \times 0.7\times 0.7

or =\ 1.54\ cm^2

Thus required area of solid = 10. 56 + 5.50 + 1.54 = 17.60 cm 2 .

Thus total surface area of remaining solid to nearest cm 2 is 18 cm 2 .

Q9 A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

1636092429678

Answer:

The required surface area is given by :

The surface area of article = Surface area of cylindrical part + 2 (Surface area of the hemisphere)

Now, the area of the cylinder =\ 2\pi rh

or =\ 2\pi \times 3.5\times 10

or =\ 70\pi \ cm^2

And the surface area of the hemisphere : =\ 2\pi r^2

or =\ 2\pi \times 3.5\times 3.5

or =\ 24.5\pi\ cm^2

Thus the required area =\ 70\pi\ +\ 2(24.5\pi)\ =\ 374\ cm^2



Some More Information About NCERT Solutions for Class 10 Maths Exercise 13.1

In NCERT syllabus for Class 10 Maths chapter 13 exercise 13.1 we have covered that the surface of a solid object ismeasurement of the overall area that the object's surface takes up and the curved surface of an object is that includes the area of all the curved surfaces and not the flat surfaces exampl-cone without the base.

Also Read| Surface Areas and Volumes Class 10 Notes

Benefits of NCERT Solutions for Class 10 Maths Exercise 13.1

  • Class 10 Maths chapter 13 exercise 13.1 will be helpful in further exercise of the chapter 10 surface area and volume
  • Class 10 Maths chapter 13 exercise 13.1 covers the knowledge which we can use in our real life
  • Surface area and volume are an important part of mechanical , mechtronic , tool , physics engineering
  • We can also use Class 10 Maths chapter 13 exercise 13.1 as base for the cellular changes in the volume of cell

Key Features For Class 10 Maths Chapter 13 Exercise 13.1

  • Step-by-Step Solutions: Clear and detailed explanations for each problem in Ex 13.1 class 10, ensuring students understand the methodology.
  • Conceptual Understanding: Explanation of area and volume concepts involved in the exercises, aiding students in grasping the underlying principles are discussed in class 10 maths ex 13.1.
  • Variety of Problems: In class 10 ex 13.1, diverse types of problems, offering a broad spectrum of challenges to reinforce understanding.
  • Visual Aids, Diagrams, and Examples: Use of visual representations, diagrams, and real-life examples to simplify complex concepts and aid visual learners.
  • Application-Based Problems: In 10th class maths exercise 13.1 answers, application-oriented problems that relate statistics to real-world scenarios, fostering practical understanding and problem-solving skills.

Also See:

NCERT Solutions Subject Wise

Frequently Asked Question (FAQs)

1. What is the curved surface area of the hemisphere ?

Curved surface area of hemisphere used is =2πr²

2. What is the curved surface area of the cylinder u?

Curved surface area of hemisphere used in  2πrl

3. What is the most commonly used value of pi used in Exercise 13.1 Class 10 Maths ?

Most commonly used value of pi used in exercise 13.1 Class 10 Maths is 22/7

4. How can we use surface area in real life? Give some examples ?

We can use surface area in many places in our daily life, for example identifying the amount of paint require to paint object , determining the cost of things like clothes , covers and canvas tents 

5. What is the total number of example that have been solved before theExercise 13.1 Class 10 Maths.

The total number of example  that have been solved before the class 10 Maths chapter 13 exercise 13.1 is four 

6. What is the total number of questions in the NCERT solutions for Class 10 Maths chapter 13 exercise?

The total number of questions in the NCERT solutions for Class 10 Maths chapter 13 exercise is nine.

7. What kind of questions are asked in 10 Maths chapter 13 exercise 13.1?

There are many basic question in which we have to find the total surface of combination of solid or real life objects such as tents , capsules toys etc but some are direct that only ask about the solid  

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