A-Level Further Maths E2-06 Volumes of Revolution: Volume of a Sphere

[theo]

Thanks for doing Further Maths content as well, much appreciated.

[tagidinihousia]

You came in at the perfect time I literally have homework for tomorrow about this and didn’t get it

[forthrightgambitia]

This is what I wanted to know when I was 15 and that 4/3 seemed really bizarre.

[sheldonwu]

Brilliant. However, I was worried that the volume might turn out to be zero. Because the shaded region has half in negative x axis and half in positive x axis. But still, it turned out to be a positive volume.

[gopalgeorge]

Why is there such a massive difference between an A and A* (in terms of marks and difficulty)

[nosir]

If the shaded region is rotated about the y-axis instead, would the limit you use be r (up the y-axis) and -r (down the y-axis) then? Of course, it would make no difference in this example but for say, deriving the same equation for the volume of a cone, where you have a right-angled triangle of width r and a height of h, and if it were to be swept around the y axis, would your limits be h and 0?

[joshplayz]

If you integrate a circle like this, will it always ignore the area below the curve? Because otherwise that would just give a negative area, and it would cancel out, would it not?