Volume of Curves Question

[leflyi]

1. A solid sphere of radius 6 cm has a cylindrical hole of radius 1 cm bored through its centre. What is the volume of the remainder of the sphere?

How to begin to tackle this question, I began by determining sphere volume then subtracting the cylindrical value. However, their is no height.. The book implies a annulus in the back, however I may be missing something quite elementary..

Any insight?

leflyi

[b^3]

Draw a cross-section of the remaining area (so draw a circle and a rectangle cutting through it). Then you should be able to form a volume of revolution around the axis, working with the upper (right) equation and the lower (left) equation.

Now the upper equation will be that of the circle, and the lower equation will be that of the straight line (well a constant x=1 in this case). You can get your terminals from for the volume of revolution where the two equations meet. Then just apply your formula for the volume of revolution around the axis.

EDIT: Also on a kinda related note, this is similar to an assignment question I had for second year uni maths, except we had to use double integrals and such

[BubbleWrapMan]

Another way is to find the volume of the 'cap' at the top (i.e. integrate from the higher intersection point to 6 with respect to ), double it, then add the volume of the cylinder, which doesn't need integration.

Oh, and then subtract that from the whole sphere.

[AsianNerd]

you could also just used a volume equation of sphere and subtract volume of cylinder... but i guess ur meant to use integration... thsi question is from the maths quest 12 boom

[BubbleWrapMan]

You can't subtract the cylinder, since there's still the 'caps' at the top and bottom.

[satya]

is this question from any book or??