Mathematics teacher of a school took her 10th standard students to show Red fort. It
was a part of their Educational trip. The teacher had interest in history as well. She
narrated the facts of Red fort to students. Then the teacher said in this monument one
can find combination of solid figures. There are 2 pillars which are cylindrical in shape.
Also 2 domes at the corners which are hemispherical.7 smaller domes at the centre.
Flag hoisting ceremony on Independence Day takes place near these domes.
a) How much cloth material will be required to cover 2 big domes each of radius 2.5
metres? (Take Π= 22/7)
a) 75m
2 b) 78.57m
2 c) 87.47m
2 d) 25.8m
2
1
b) Write the formula to find the volume of a cylindrical pillar.
a) Πr
2h b) Πrl c) Πr(l + r) d) 2Πr
1
c)
Find the lateral surface area of two pillars if height of the pillar is 7m and radius of the
base is 1.4m.
a) 112.3cm
2 b) 123.2m
2 c) 90m
2 d) 345.2cm
2
1
d)
How much is the volume of a hemisphere if the radius of the base is 3.5m?
a) 85.9 m
3 b) 80 m
3 c) 98 m
3 d) 89.83 m
3
1
e)
What is the ratio of sum of volumes of two hemispheres of radius 1cm each to the
volume of a sphere of radius 2 cm?
a) 1:1 b) 1:8 c) 8 :1 d) 1:16
Answers
Given : 2 hemispherical domes
To Find : How much cloth material will be required to cover 2 big domes each of radius 2.5metres
a) 75m2
b) 78.57m2
c) 87.47m2
d) 25.8m2
Solution:
To Cover Dome we need to cover Curved surface area only with cloth
as base is on ground
CSA of Hemisphere = 2 πr²
r = 2.5 m
CSA of one Dome = 2 π(2.5)²
CSA of two Domes = 2 x 2 π(2.5)²
= 25π m²
π = 22/7
= 25 x 22/7
= 78.57 m²
78.57 m² cloth material will be required to cover 2 big domes each of radius 2.5metres
option b is correct
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