Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?
A) has finite volume and finite surface area.
B) has finite surface area and infinite volume.
C) has finite volume and infinite surface area.
D) has infinite volume and infinite surface area.
E) None of the above is correct.

Question

Let  be the solid obtained by revolving the infinite graph of  about the x-axis for  .  Which of the following statements is correct?
A) has finite volume and finite surface area. 
B) has finite surface area and infinite volume. 
C) has finite volume and infinite surface area. 
D) has infinite volume and infinite surface area. 
E) None of the above is correct.

Quizplus · Accepted Answer

When we revolve the infinite graph about the x-axis, it will create an infinitely long cylinder with radius extending to infinity. This means that the cylinder will have infinite surface area. However, the volume of the cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height. The height of the cylinder will be the distance between the curves of the graph, which is finite. Thus, the volume of the cylinder will be finite as well. Therefore, option C is correct.

Let Be the Solid Obtained by Revolving the Infinite