Study Materials: ncert solutions

Our ncert solutions for Exercise 13.1 Class 10 maths 13. Surface Areas and Volumes - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

Solutions ⇒ Class 10th ⇒ Mathematics ⇒ 13. Surface Areas and Volumes

Exercise 13.1 Class 10 maths 13. Surface Areas and Volumes - ncert solutions - Toppers Study

Topper Study classes prepares ncert solutions on practical base problems and comes out with the best result that helps the students and teachers as well as tutors and so many ecademic coaching classes that they need in practical life. Our ncert solutions for Exercise 13.1 Class 10 maths 13. Surface Areas and Volumes - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

Exercise 13.1 Class 10 maths 13. Surface Areas and Volumes - ncert solutions - Toppers Study

CBSE board students who preparing for class 10 ncert solutions maths and Mathematics solved exercise chapter 13. Surface Areas and Volumes available and this helps in upcoming exams 2022-2023.

You can Find Mathematics solution Class 10 Chapter 13. Surface Areas and Volumes

  • All Chapter review quick revision notes for chapter 13. Surface Areas and Volumes Class 10
  • NCERT Solutions And Textual questions Answers
  • Extra NCERT Book questions Answers
  • Importatnt key points with additional Assignment and questions bank solved.

NCERT Solutions do not only help you to cover your syllabus but also will give to textual support in exams 2022-2023 to complete exercise 13.1 maths class 10 chapter 13 in english medium. So revise and practice these all cbse study materials like class 10 maths chapter 13.1 in english ncert book. Also ensure to repractice all syllabus within time or before board exams for ncert class 10 maths ex 13.1 in english.

See all solutions for class 10 maths chapter 13 exercise 13 in english medium solved questions with answers.

Exercise 13.1 class 10 Mathematics Chapter 13. Surface Areas and Volumes

13. Surface Areas and Volumes

| Exercise 13.1 |

Exercise 13.1 Class 10 maths 13. Surface Areas and Volumes - ncert solutions - Toppers Study


Chapter 13. Surface Areas and Volumes Exercise 13.1 solved solution


Q1. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

Solution: 

The volume of cube = 64 cm3

Joining two surfaces;

l = 4 + 4 = 8 cm 

b = 4 cm 

h = 4 cm 

The Surface Area of such formed cuboid = 2(lb + bh + lh)

= 2(8×4 + 4×4 + 8×4)

‚Äč= 2(32 + 16 + 32)

= 2×80

= 160 cm2

Therefore, The area obtained from this cuboid is 160 cm2

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.

Solution: 


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

Solution:

The radius of hemisphererr = 3.5 cm

The radius of conical partr = 3.5 cm

The height of conical partrh = 15.5 – 3.5 = 12 cm


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.

Solution:

The edge of cubical block = 7 cm

The maximum diameter of the blockd = 7 cm

The total surface area of block = The Area of cuboidal block + The Area of hemisphere – Area of a circle covered with hemisphere  

= 294 + 38.5 = 332.5 cm2

Therefore, total surface area of block = 332.5 cm2

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.

Solution:

Let the diameter of hemisphered = l unit

And the edge of cubea = l unit

(Hence, diameter of hemisphere and the edge of cube are same)

Total surface Area of remaining solid = Area of cuboidal block + Area of hemisphere – Area of a circle covered with hemisphere  

Q6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

Solution:

The height of cylinder = length of capsule – 2(2.5 mm)

= 14 – 5 [Hence diameter = 2.5 mm]

= 9 mm

Total Surface area of capsule = 2(curve surface area of hemisphere) + curve surface area of cylinder

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 m2. (Note that the base of the tent will not be covered with canvas.)

Solution:

 

The diameter of the cylindrical part of tent = 4 m

So, radius = 2 m

The height of cylindrical part = 2.1 m

The slant height of cone = 2.8 m

And radius = 2 m

The area of required canvas = the curved surface area of cylindrical part + curved surface area of conical part

= 2πrh + πrl

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 cm2.

Solution:

The height of cylinder h = 2.4 cmcm

The diameter of cylinder = 1.4 cm

So, radius of cylinder = 0.7 cm

The height of hollowed out = 2.4 cm

Radius = 0.7 cm  

Total surface area of remaining solid = Curved surface area of cylinder + curved surface area of cone + Area of the bottom of solid

 = 2πrh + πrl + πr2

 = πr(2h + l + r)

The total surface area of the remaining solid to the nearest cm2 = 18 cmAnswer

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.

Solution: 

The height of cylinder = 10 cm

The radius (r) of base = 3.5 cm

The radius (r) of hemisphere = 3.5 cm

Total surface area = Curved surface area of cylinder + Curved surface area of top of hemisphere + Curved surface area of bottom of hemisphere

= 2πrh + 2πr2 + 2πr2

= 2πr(h h + rr + rr )

= 2πr(hh + 2rr)

Total surface area is 374 cm2

Select Your CBSE Classes

Important Study materials for classes 06, 07, 08,09,10, 11 and 12. Like CBSE Notes, Notes for Science, Notes for maths, Notes for Social Science, Notes for Accountancy, Notes for Economics, Notes for political Science, Noes for History, Notes For Bussiness Study, Physical Educations, Sample Papers, Test Papers, Mock Test Papers, Support Materials and Books.

 

 

Mathematics Class - 11th

NCERT Maths book for CBSE Students.

books

Study Materials List:

Solutions ⇒ Class 10th ⇒ Mathematics
1. Real Numbers
2. Polynomials
3. Pair of Linear Equations in Two Variables
4. Quadratic Equations
5. Arithmetic Progressions
6. Triangles
7. Coordinate Geometry
8. Introduction to Trigonometry
9. Some Applications of Trigonometry
10. Circles
11. Constructions
12. Areas Related to Circles
13. Surface Areas and Volumes
14. Statistics
15. Probability

Topper's Study

New Books