This presentation is solution to the previous presentation, i.e., Pem Mati. Pem mati was a dancer in the kingdom of Nizam. Out of the famous Seven Tombs located near Golconda Fort, Hyderabad, Pem Mati tomb is one. She was also called as Premamati by a Nizam ruler. The Seven Tombs, also known as Qutubshahi Tombsis one of the historical heitage place one can visit in Hyderabad.

1. Tomb of ”Pem Mati” (Premamati)
Assignment 2
T Sree Vamsi, Pradyumna M Dinni
November 2016
1 Solutions to Problem Statement
1.1 Given dimensions
The given dimensions are:
a) Total height of the tomb = 13.7m
b) The length and width of the cuboid = (12.7m x 12.7m)
c) Two angles of elevation( all angles are in degrees) i.e., 370
and 39.120
.
d) The height of one of the four cylindrical regions(the regions below the
smaller domes) = 0.7m
Figure 1: Figure of (d)
1.2 Calculation of required dimensions
The required dimensions are:
a) Height of the cuboid
b) Radius of the bigger hemispherical dome
c) Volume of the cuboid
d) Radius of the smaller dome(one among four smaller domes)
e) Total volume of the tomb(i.e., Volume of cuboid + Volume of hemispher-
ical dome)
1

2. 1.3 (a) Height of the cuboid
Given, AC=15m, angle(ACB)= 370
Using basic trignometry, tan(370
) = AB/AC
Therefore, AB = ACtan(370
)
As AC = 15m, AB = 11.30m
1.4 (b) The radius of the bigger hemispherical dome
As given total height of the tomb = 13.7m and we have calculated the height
of the cuboid, i.e., Height of the cuboid = 11.30m.
As the radius of the dome + height of the cuboid = Total height of the tomb.
Therefore,
2

3. Radius of the hemispherical dome = Total height of the tomb - height of the
cuboid. Therefore, Radius of the dome = 13.7m - 11.3m = 2.4m.
The Radius of the bigger hemispherical dome = 2.4m.
1.5 (c) Volume of the cuboid
Volume of the cuboid = (length)x(width)x(height).
We are given length and width and we have caluculated the height.
Therefore,
Volume of the Cuboid = (12.7x12.7x11.3) m3
.
Volume of the cuboid = 1822.577 m3
.
3

4. 1.6 (d) Radius of the smaller dome(one among the four).
Given,
BM = 0.7m, Angle of inclination, angle(ACD) = 39.120
, AC = 15m and we
have calculated AB = 11.3m.
Again, using trigonometry,
tan(39.120
) = AD/AC
AD = ACtan(39.120
)
Therefore, AD = 12.2m.
And, AB+BM+MB = AD = 12.2m.
11.3m + 0.7m + Diameter of the smaller dome = 12.2m
Therefore,
Radius of the smaller dome = 0.2/2 = 0.1m
Radius of the smaller dome = 0.1m.
1.7 (e) Total Volume
Total volume of the tomb = Volume of the cuboid + volume of the hemispherical
dome.
4

5. Total volume = lxbxh + 2/3 πr3
We have length, width and height of the cuboid and calculated the Radius
of the dome.
Therefore on substituting these values,
Total volume = 12.7 x 12.7 x 11.3 + 2/3 x22/7 x(2.4)3
Total volume = 1851.541 m3
.
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