Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 9 Mathematics 13. Surface Areas and Volumes to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 9 Mathematics 13. Surface Areas and Volumes to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 13.4. Whether you are studying for board exams or mid-term exams, 9 Mathematics Chapter 13. Surface Areas and Volumes solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise 13.4
Assume π = 22/7 , unless stated otherwise.
Q1. Find the surface area of a sphere of radius:
(i) 10.5 cm (ii) 5.6 cm (iii) 14 cm
Solution:
Q2. Find the surface area of a sphere of diameter:
(i) 14 cm (ii) 21 cm (iii) 3.5 m
Solution:
(i) Surface area of sphere = 4πr2
Q3. Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
Solution:
Total surface area of hemisphere = 3πr2
⇒ 3 × 3.14 × 10 × 10
⇒ 3 × 314
⇒ 942 cm2
Q4. 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.
Solution:
Surface area of sphere = 4πr2
Q5. 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.
Solution:
Curved surface area of hemisphere = 2πr2
Q6. Find the radius of a sphere whose surface area is 154 cm2.
Solution:
Area = 154 cm2
Surface area of sphere = 4πr2
Q7. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.
Solution:
Let the diameter of earth = x
Q8. 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.
Solution:
Inner radius = 5 cm, width = 0.25 cm, radius = 5.25 cm
Curved surface area of hemisphere = 2πr2
⇒ 44 × 0.75 × 5.25
⇒ 173.25
Q9. A right circular cylinder just encloses a sphere of
radius r (see Fig. 13.22). Find
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).
Solution:
Radius of sphere = r, radius of cylinder = r + r = 2r
(i) surface area of sphere = 4πr2
(ii) curved surface area of cylinder = 2πrh
⇒ 2πr(2r)
⇒ 4πr2
Exercise 13.4 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 9 Mathematics Chapter 13. Surface Areas and Volumes solutions help you understand the core concepts and practice effectively.
Revision is the key to exam success. Our notes for 9 Mathematics highlight important formulas, key definitions, and exam-ready points from Chapter 13. Surface Areas and Volumes. These quick revision notes make last-minute preparation easy.
Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 13.4 include complete solutions for 9 Mathematics Chapter 13. Surface Areas and Volumes exercises. With step-by-step answers, you gain clarity and confidence to attempt similar exam questions.
To boost your preparation, we also provide additional important questions with answers. These are prepared from previous year board papers, sample papers, and important concepts of Chapter 13. Surface Areas and Volumes. Practicing these ensures you are well-prepared for both board and mid-term exams.
Our Exercise 13.4 are useful for both board exams and mid-term exams. For 9 Mathematics, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 13.4 for 9 Mathematics Chapter 13. Surface Areas and Volumes are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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