Q) The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of Indian Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BCE. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha. .It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal structure mounted on it. (Take π = 22/7)

1. Calculate the volume of the hemispherical dome if the height of the dome is 21 m:

a) 19404 cu. m.      b) 2000 cu .m.    c) 15000 cu. m.      d) 19000 cu. m

2. The formula to find the Volume of Sphere is:

a) 2/3 π r3.             b) 4/3 π r3.                c) 4 π r2.                   d) 2 π r2

3. The cloth require to cover the hemispherical dome if the radius of its base is 14m is:

a) 1222 sq.m.      b) 1232 sq.m.       c) 1200 sq.m.       d) 1400 sq.m

4. The total surface area of the combined figure i.e. hemispherical dome with radius 14m and cuboidal shaped top with dimensions 8m 6m 4m is:

a)1200 sq. m.       b) 1232 sq. m.       c) 1392 sq.m.      d) 1932 sq. m

5. The volume of the cuboidal shaped top is with dimensions mentioned in question 4:

a) 182.45 m3.         b) 282.45 m3.         c) 292 m3.                d) 192 m3

Ans:

1. Hemispherical dome’s volume:

The volume of hemispherical cup is =

Since the height of the dome is the radius of the dome,

Therefore,

Volume of hemispherical cup =

=

=

= 44 x 21 x 21 = 924 x 21 = 19404 m3

Hence, option a) is correct option.

2. Formula for Volume of Sphere:

Since the Volume of Sphere is calculated by:

Here r is the radius of the sphere.

This is the formula for calculating the sphere’s volume.

Therefore option (b) is correct.

3. Cloth area to cover the hemispherical dome:

The curved surface area of hemispherical dome is =

Since r = 14 m, therefore Curved surface area of hemispherical dome =

=

= 2 x 22 x 2 x 14

= 88 x 14 = 1232 m2

Hence, option b) is correct option.

4. Total surface area of the combined figure:

Since the surface area of hemispherical dome = surface area of hemispherical base + surface area of cuboidal top

Radius = 14 m,  Cuboidal top’s dimensions (l, b,h) = 8 x 6 x 4 m

A) Surface area of hemispherical dome = 1232 cm2 (calculated in part 3)

B) Surface area of cuboid (without base) = surface area of walls + area of top

= 2 h l + 2 h b + l b

= 2 (4) (8) + 2 (4) (6) + 8 × 6

= 64 +  48 + 48  = 160 m2

Surface area of hemispherical dome = 1232 + 160 = 1392 m2

Hence, option c) is correct option.

5. Volume of the cuboidal top:

Volume of the  cuboid = l b h

Since, Cuboidal top’s dimensions (l, b,h) = 8, 6, 4 m

Therefore, Volume of the cuboidal top = 8 x 6 x 4 = 192 m 2

Hence, option d) is correct option.

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