(a) Right circular cylinder:

Volume of right circular cylinder can be found by the revolving the base radius about  axis.

Hence, .

.

Thus, option (ii)  is correct choice.

(b) Ellipsoid:

Equation of the vertical ellipse with axes  and  is .

Volume of right ellipsoid can be found by the revolving the base radius about  axis.  

Hence, .

.

Here value of  varies from  to .

Therefore, volume of the ellipsoid is .

Thus, option (iv)  is correct choice.

(c) Sphere:

Outer part of the sphere is alike the circle.

Equation of the circle center at origin and with radius  is .

Volume of sphere can be found by the revolving the base radius about  axis. Hence, .

.

Here value of  varies from  to .

Therefore, volume of the ellipsoid is .

Thus, option (iii)  is correct choice.

(d) Right circular cone:

Consider cone with base radius  and height .

Observe the figure,

Radius of the region is .

.

Therefore, volume of the ellipsoid is .

Thus, option (i)  is correct choice.

(d) Torus:

Radius of the cross section of torus is  and distance from the center of its cross section to

the axis of the torus is .

Inner part is a circle .

Observe the figure:

.

Here outer radius of the region is .

Inner radius of the region is .

Therefore, volume of the torus is .

Thus, option (v)  is correct choice.

(a) Option (ii).

(b) Option (iv).

(c) Option (iii).

(d) Option (i).

(e) Option (v).