Question

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.
i)
How much cloth material will be required to cover 2 big domes each of radius
2.5 metres? (Take n = 22/7)
1
ii)
a) 75m2
by 78.57m2 c) 87.47m2
d) 25.8m2
b)
Write the formula to find the volume of a cylindrical pillar.
а) Пr?h
b) nr
c) Mr(1+r)
d) 2017
1
Find the lateral surface area of two pillars if height of the pillar is 7m and
radius of the base is 1.4m.
a) 112.3cm2
b) 123.2m2
c) 90m2
d) 345.2cm?
iv)
How much is the volume of a hemisphere if the radius of the base is 3.5m?
a) 85.9 m
b) 80 m3
c) 98 m
d) 89.83 m​

Answer 1

Step-by-step explanation:

(i) Area of hemisphere = 2πr2

= 2× 2πr2

= 2×2×22/7× (2.5)2

= 2×2×22/7×6.25

= 550/7

= 78.57 m2

(ii) Volume of cylinder = πr2h

(iii) Height of pillars = 7m

Radius of pillars = 1.4 m

Lateral surface area of cylinder = 2πrh

2×2πrh ( as we have two find area of two pillars )

= 2×2×22/7 × 1.4 × 7

= 2×2×22×1.4

= 88 × 1.4

123.2 m2

(iv) Radius of hemisphere = 3.5 m

Volume of hemisphere = 2/3π r3

= 2/3 × 22/7 × ( 3.5 ) 3

= 2/3 × 22/7 × 3.5 × 3.5 × 3.5

= 89.83 m3

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