find the volume

Question

A ball of radius 16 has a round hole of radius 6 drilled through its center.

Find the volume of the resulting solid.

Answer 1

ball has a volume of 4/3(pi(16^3)

hole has a volume of slightly more than 3399.1

subtract that from volume of the sphere = 17,157.2

to get about 13,758

It's slightly less though

Answer 2

a method is as follows

1. use spherical coordinates to find volume of top cone and cap with radius of 16, cap starts at z=2√55 which is to say cos(Φ)=(√55)/8 ,,,,volume top side cone and cap=VCC=∫∫∫ρ²sinΦ*dρ*dΦ*dθ. ,,,where ρ limits are 0 to 16,,,,, Φ limits 0 to cos^-1((√55)/8),,,, θ limits 0 to 2π.
2. For VC=volume cap top side, VC=VCC minus cone volume. Where cone volume=(1/3)*36π*2√55
3. Add to VC the top cylinder volume = 36π*2√55
4. multiply #3 by two to have volume of hole piece cut from sphere
5. subtract #4 from (4/3)*16³π

computes to 17,157.28 (sphere volume) minus 3,488.08 (cylinder hole cut out volume)=13,669.20 (volume left intact)=answer,,,,,,,,Note:3,488.08 = volume from #4 above, that is cylinder volume plus top and bottom cap volumes=3,488.08