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| PAGE: 456 | SET: Exercises | PROBLEM: 69 |
(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).
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