As a hardworking student, plagued by too much homework, you spend all night doing math homework. By 6am, you imagine yourself to be a region bounded by

Question

y=5x2
x=0
x=3
y=0
As you grow more and more tired, the world begins to spin around you. However, according to Newton, there is no difference between the world spinning around you, and you spinning around the world. Unfortunately, you are so tired that you think the world is the x-axis. What is the volume of the solid you (the region) create by spinning about the x-axis?

Answer 1

I am not a fan of coating a simple question in cutesy wording, so here is the question the way it would appear in my assignment.

Find the volume when the region bounded by
y = 5x^2, x = 0 , x = 3 and y = 0 is rotated about the x-axis

V = π∫ 25x^4 dx from x = 0 to x = 3
= π [ 5x^5] from 0 to 3
= π(5(3^5) - 0)
= 1215π