Questions 1-10 from Section 7.1

1. R is bounded by , and ; we rotate R around the x-axis.

2. R is bounded by , and ; we rotate R around the y-axis.

3. R is bounded by  , , and ; we rotate R around the x-axis.

Here is the same solid again cut through the middle to see its cross-section.

4. R is bounded by  , , and ; we rotate R around the y-axis.

Again we cut to take a look at the hidden cross-section.

5(a). R is bounded by , , and ; we rotate R around the x-axis.

5(b). R is bounded by , , and ; we rotate R around the y-axis.

6(a). R is bounded by and ; we rotate R around the x-axis.

Cross-section (compare with 3 above):

6(b). R is bounded by and ; we rotate R around the y-axis.

Cross-section (compare with 4 above):

7(a). R is bounded by and ; we rotate R around the x-axis.

We cut through the middle to see its cross-section:

7(b). R is bounded by and ; we rotate R around the y-axis.

The cross-section:

8(a). R is bounded by , ,   and   ; we rotate R around the x-axis.

The cross-section:

8(b). R is bounded by , ,   and   ; we rotate R around the y-axis.

The cross-section:

9(a). R is bounded by , ,   and   ; we rotate R around the x-axis.

The inner structure can be seen below:

Just a change of viewpoint (same cross section of the same solid):

9(b). R is bounded by , ,   and   ; we rotate R around the y-axis.

Not much can be seen - so we cut in half again to see better:

10(a). R is bounded by and   ; we rotate R around the x-axis.

The inner structure revealed:

10(b). R is bounded by and   ; we rotate R around the y-axis.

Crosscut to see inside:

© S.Kalajdzievski