UPSC CDS Math Volume and Surface Area Questions

Let r be the radius of the base of the cylinder.
∴ Height of the building = 3r
Height of the hemispherical dome = Radius of the hemispherical dome = r
∴ Height of the cylindrical portion of the building =3r−r=2r
Volume of air in the building
=67

1

21

=

1408

21

m3
∴

2

3

πr3+πr2×2r=

1408

21

⇒

8

3

πr3=

1408

21

⇒r3=

1408×7×3

21×22×3

=8
⇒r=2m
∴ Height of the building
=3×2=6m