Gujarat Board Textbook Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.8

Gujarat Board Textbook Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.8

GSEB Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.8

Question 1.
Find the volume of a sphere whose radius is ∝

Question 2.
Find the amount of water displaced by a solid
spherical ball of diameter
1. 28 cm
2. 0.21m
Solution:

Question 3.
The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm³?
Solution:

2. Density = 8.9 g per cm³
∴ Mass of the ball = Volume x Density
= 38.808 x 8.9
= 345.39 g (approx.)

Question 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:

Question 5.
How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?
Solution:

Question 6.
A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
Solution:
Inner radius (r) = 1 m
Thickness of iron sheet = 1 cm = 0.01 m
∴ Outer radius (R) = Inner radius (r) + Thickness of iron sheet
= 1 m + 0.01 m = 1.01 m
∴ Volume of the iron used to make the tank

Question 7.
Find the volume of a sphere whose surface area is 154 cm².
Solution:

Question 8.
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of 498.96. If the cost of whitewashing is 2.00 per square meter, find the
1. inside surface area of the dome,
2. the volume of the air inside the dome.
Solution:

Question 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
1. radius r’ of the new sphere,
2. the ratio of S and S’.
Solution:

Question 10.
A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?
Solution:

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