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 = 13.7mb) 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 cuboidb) Radius of the bigger hemispherical domec) Volume of the cuboidd) 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)

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1.3 (a) Height of the cuboid

Given, AC=15m, angle(ACB)= 370

Using basic trignometry, tan(370) = AB/ACTherefore, 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 heightof 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,

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Radius of the hemispherical dome = Total height of the tomb - height of thecuboid. 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.

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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/ACAD = ACtan(39.120)Therefore, AD = 12.2m.And, AB+BM+MB = AD = 12.2m.11.3m + 0.7m + Diameter of the smaller dome = 12.2mTherefore,Radius of the smaller dome = 0.2/2 = 0.1mRadius of the smaller dome = 0.1m.

1.7 (e) Total Volume

Total volume of the tomb = Volume of the cuboid + volume of the hemisphericaldome.

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Total volume = lxbxh + 2/3 πr3

We have length, width and height of the cuboid and calculated the Radiusof 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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