*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 11.
NCERT Solutions for Class 9 Maths Chapter 13 Surface Area and Volume Exercise 13.8 is made available here for the students in PDF format. These problems in NCERT Solutions have been solved by experienced Maths experts considering the understanding and grasping capabilities of the students. All the solutions for 9th Maths subjects are in accordance with the NCERT syllabus and guidelines and are helpful for the students to score good marks.
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Access Other Exercise Solutions of Chapter 13 Surface Areas and Volumes
Exercise 13.1 solution (9 questions)
Exercise 13.2 solution (8 questions)
Exercise 13.3 solution (9 questions)
Exercise 13.4 solution (5 questions)
Exercise 13.5 solution (5 questions)
Exercise 13.6 solution (8 questions)
Exercise 13.7 solution (9 questions)
Exercise 13.9 solution (3 questions)
Access Answers to NCERT Class 9 Maths Chapter 13 Surface Areas and Volumes Exercise 13.8
1. Find the volume of a sphere whose radius is
(i) 7 cm (ii) 0.63 m
(Assume π =22/7)
Solution:
(i) Radius of the sphere, r = 7 cm
Using, Volume of sphere = (4/3) πr3
= (4/3)×(22/7)×73
= 4312/3
Hence, the volume of the sphere is 4312/3 cm3
(ii) Radius of the sphere, r = 0.63 m
Using, volume of sphere = (4/3) πr3
= (4/3)×(22/7)×0.633
= 1.0478
Hence, the volume of the sphere is 1.05 m3 (approx).
2. Find the amount of water displaced by a solid spherical ball of diameter
(i) 28 cm (ii) 0.21 m
(Assume π =22/7)
Solution:
(i) Diameter = 28 cm
Radius, r = 28/2 cm = 14cm
Volume of the solid spherical ball = (4/3) πr3
Volume of the ball = (4/3)×(22/7)×143 = 34496/3
Hence, the volume of the ball is 34496/3 cm3
(ii) Diameter = 0.21 m
Radius of the ball =0.21/2 m= 0.105 m
Volume of the ball = (4/3 )πr3
Volume of the ball = (4/3)× (22/7)×0.1053 m3
Hence, the volume of the ball = 0.004851 m3
3.The diameter of a metallic ball is 4.2cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3? (Assume π=22/7)
Solution:
Given,
Diameter of a metallic ball = 4.2 cm
Radius(r) of the metallic ball, r = 4.2/2 cm = 2.1 cm
Volume formula = 4/3 πr3
Volume of the metallic ball = (4/3)×(22/7)×2.1 cm3
Volume of the metallic ball = 38.808 cm3
Now, using the relationship between density, mass and volume,
Density = Mass/Volume
Mass = Density × volume
= (8.9×38.808) g
= 345.3912 g
Mass of the ball is 345.39 g (approx).
4. 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?
Solution:
Let the diameter of the earth be “d”. Therefore, the radius of the earth will be d/2
The diameter of the moon will be d/4, and the radius of the moon will be d/8
Find the volume of the moon :
Volume of the moon = (4/3) πr3 = (4/3) π (d/8)3 = 4/3π(d3/512)
Find the volume of the earth :
Volume of the earth = (4/3) πr3= (4/3) π (d/2)3 = 4/3π(d3/8)
Fraction of the volume of the earth is the volume of the moon
Answer: The volume of the moon is 1/64 volume of the earth.
5. How many litres of milk can a hemispherical bowl of diameter 10.5cm hold? (Assume π = 22/7)
Solution:
Diameter of hemispherical bowl = 10.5 cm
Radius of hemispherical bowl, r = 10.5/2 cm = 5.25 cm
Formula for volume of the hemispherical bowl = (2/3) πr3
Volume of the hemispherical bowl = (2/3)×(22/7)×5.253 = 303.1875
Volume of the hemispherical bowl is 303.1875 cm3
Capacity of the bowl = (303.1875)/1000 L = 0.303 litres(approx.)
Therefore, the hemispherical bowl can hold 0.303 litres of milk.
6. A hemi spherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank. (Assume π = 22/7)
Solution:
Inner Radius of the tank, (r ) = 1m
Outer Radius (R ) = 1.01m
Volume of the iron used in the tank = (2/3) π(R3– r3)
Put values,
Volume of the iron used in the hemispherical tank = (2/3)×(22/7)×(1.013– 13) = 0.06348
So, the volume of the iron used in the hemispherical tank is 0.06348 m3.
7. Find the volume of a sphere whose surface area is 154 cm2. (Assume π = 22/7)
Solution:
Let r be the radius of a sphere.
The surface area of the sphere = 4πr2
4πr2 = 154 cm2 (given)
r2 = (154×7)/(4 ×22)
r = 7/2
Radius is 7/2 cm
Now,
Volume of the sphere = (4/3) πr3
8. A dome of a building is in the form of a hemi sphere. From inside, it was white-washed at the cost of Rs. 4989.60. If the cost of white-washing isRs20 per square meter, find the
(i) inside surface area of the dome (ii) volume of the air inside the dome
(Assume π = 22/7)
Solution:
(i) Cost of white-washing the dome from inside = Rs 4989.60
Cost of white-washing 1m2 area = Rs 20
CSA of the inner side of dome = 498.96/2 m2 = 249.48 m2
(ii) Let the inner radius of the hemispherical dome be r.
CSA of inner side of dome = 249.48 m2 (from (i))
Formula to find CSA of a hemisphere = 2πr2
2πr2 = 249.48
2×(22/7)×r2 = 249.48
r2 = (249.48×7)/(2×22)
r2 = 39.69
r = 6.3
So, the radius is 6.3 m
Volume of air inside the dome = Volume of hemispherical dome
Using the formula, the volume of the hemisphere = 2/3 πr3
= (2/3)×(22/7)×6.3×6.3×6.3
= 523.908
= 523.9(approx.)
Answer: The volume of air inside the dome is 523.9 m3.
9. 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 Sand S’.
Solution:
Volume of the solid sphere = (4/3)πr3
Volume of twenty seven solid sphere = 27×(4/3)πr3 = 36 π r3
(i) New solid iron sphere radius = r’
Volume of this new sphere = (4/3)π(r’)3
(4/3)π(r’)3 = 36 π r3
(r’)3 = 27r3
r’= 3r
Radius of the new sphere will be 3r (thrice the radius of the original sphere)
(ii) Surface area of the iron sphere of radius r, S =4πr2
Surface area of the iron sphere of radius r’= 4π (r’)2
Now
S/S’ = (4πr2)/( 4π (r’)2)
S/S’ = r2/(3r’)2 = 1/9
The ratio of S and S’ is 1: 9.
10. A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine (in mm3) is needed to fill this capsule? (Assume π = 22/7)
Solution:
Diameter of capsule = 3.5 mm
Radius of capsule, say r = diameter/ 2 = (3.5/2) mm = 1.75mm
Volume of spherical capsule = 4/3 πr3
Volume of spherical capsule = (4/3)×(22/7)×(1.75)3 = 22.458
Answer: The volume of the spherical capsule is 22.46 mm3.
This exercise features ten questions based on the volume of the sphere. For all exercise questions for NCERT Solutions for Class 9 Maths Chapter 13, reach us at BYJU’S. Solve previous year question papers along with solutions to get an idea of the question pattern. You can also get here notes and books along with tips and tricks for learning the 9th standard syllabus of Maths and Science.
The questions in NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.8 includes short and long answers question which should be practised for a better score. NCERT solutions provide answers to all the problems of subjects like Maths and Science for all the classes.
Key Features of NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volume Exercise 13.8
Solving these solutions helps students to:
- Improves their speed in answering problems.
- Pupils can assess their problem-solving ability and prepare accordingly.
- Helps students to find the volume of the right circular cone with given specifications.
- The method of finding the radius of the sphere can be known.
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