Mathematics teacher of a school took her class 9th students to show Red fort. It was a part of their
educational trip. The teacher has 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.
Seven smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place
(i) How much cloth material will be required to cover 2 big domes each of radius 2.5metres?
(Take ? =
22)
7
a) 75m2
b) 78.57m2
c) 87.47m2
d) 25.8m2
(ii) Write the formula to find the volume of a cylindrical pillar.
a) Πr2
h b) Πrl c) Πr(l+r) d) 2Πr
(iii) Find the lateral surface area of two pillars if height of the pillar is 7m and radius of the base of
the radius of the base is 1.4m.
a) 112.3cm2
b) 123.2m2
c)90m2
d)345.2cm2
(iv) How much is the volume of a hemisphere if the radius of the base is 3.5m?
a) 85.9m3
b) 80m3
c) 98m3
d)89.3m3
(v) What is the ratio of sum of volumes of two hemispheres of radius 1cm each to the volume of
a sphere of radius 2cm?
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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Answer:
How much is the volume of a hemisphere if the radius of the base is 3.5m?
a) 85.9m3
b) 80m3
c) 98m3
d)89.3m3