19.
Case study based – III
Sanchi Stupa is a Buddhist complex in Raisen District of the state of Madhya Pradesh. A renowned
architect prepared a small-scale model which is an exact replica of the Stupa. The diameter of the
hemispherical dome is 42 cm. The dome is filled with clay. Three chhatravalis are fixed on the top of the
dome. These chhatravalis have radii 2.1cm, 1.4cm and 0.7cm respectively. One Oopri Pradakshina Path
is attached all around the dome. The outer diameter of this path is 49cm.
Based on the above situation, answer the following questions (attempt any four):
The volume of clay used to prepare the dome is
(a) 16816 cm3
717151 cm3
(c) 19404 cm3
(d) 21105 cm
(ii)
The architect was asked to cover the top most chhatraval is by a conical chhatra having radius same as that of the chhatravali and height 2.4cm. Find the area of the silk cloth required to prepare the chhatra.
(a) 4.2 cm?
(b) 5.5 cm2
40 6.25 cm2
(d) 7.5 cm
Answers
Answer:
(i) (c)19404cm³
Step-by-step explanation:
Volume of the Dome(Hemisphere)= 2/3∏r³
r= 42/2cm
= 21cm
Substituting,
= 2/3 x 22/7 x 21 x 21 x 21
= 44 x 441 (By cancelling 21 by 7 and the remaining 3 by 3)
Multiplying,
= 19404 cm³
Given : The diameter of the hemispherical dome is 42 cm. The dome is filled with clay.
To Find : The volume of clay used to prepare the dome is
(a) 16816 cm³
b) 717151 cm³
(c) 19404 cm³
(d) 21105 cm³
Solution:
diameter of the hemispherical dome is 42 cm
=> Radius of the hemispherical dome is 42/2 = 21 cm
Volume of hemisphere = (2/3)πR³
π = 22/7
= (2/3)(22/7) 21³
= 44 * 21²
= 19404 cm³
volume of clay used to prepare the dome is 19404 cm³
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