help? cylinders method?

Question

Answer 1

(1)

Step 1:

The curve equations are , 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 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 .

Answer 2

(2)

Step 1 :

The curve equations are , and -axis.

Method of Cylinders :

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

Here .

Solve the function for x in terms of .

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.

Answer 3

(3)

Step 1:

The curve equations are , and -axis.

Method of Cylinders :

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

Here .

If then .

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

.

The volume of the solid is cubic units.

Solution :

The volume of the solid is cubic units.

Answer 4

(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 .

Solve the function for in terms of .

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.