(1)

Step 1:

The curve equation is , and -axis.

Method of Rings :

The volume of the solid obtained by rotating about -axis, the region of the curve  from  to is

..

Here .

Substitute in the above.

The limits of integration are and .

The volume of the solid obtained by rotating about -axis, bounded by the curve and from  to is

The volume of the solid is .

Solution :

The volume of the solid is .

(2)

Step 1:

The curve equation is , and -axis.

Method of Cylinders :

The volume of the solid obtained by rotating about -axis, the region of the curve  from  to is

Here the curve is .

Find the value of x for .

\ \

The volume of the solid is cubic units.

Solution :

The volume of the solid is cubic units.

(4)

Step 1:

The curve equation is , and -axis.

Method of Cylinders :

The volume of the solid obtained by rotating about -axis, the region of the curve  from  to is

Here .

Find the value of x for .

The volume of the solid obtained by rotating about -axis, bounded by the curve and from  to is

The volume of the solid is .

Solution :

The volume of the solid is .

(3)

Step 1:

The curve equation is , and -axis.

Method of Cylinders :

The volume of the solid obtained by rotating about -axis, the region of the curve  from  to is

.

Here .

Substitute in above.

Here limits are and .

The volume of the solid obtained by rotating about -axis, bounded by the curve  from  to is

The volume of the solid is cubic units.

Solution :

The volume of the solid is cubic units.