Friday

April 18, 2014

April 18, 2014

Posted by **Anonymous** on Monday, April 27, 2009 at 4:24pm.

I tried finding the volume of the sphere and the volume of the cyclinder then subtract however that did not work.

- Calculus -
**Reiny**, Monday, April 27, 2009 at 5:55pmthe part that is cut out,what you call a "cylinder" is not really at cylinder.

you are forgetting about the caps on each end of your 'cylinder'

we will have to use Calculus to do that

Visualize a circle, centre at the origin and radius of 12,rotating about the x-axis resulting in our sphere.

NOw visualize a drill bit of radius 3 as the x-axis, drilling out a hole.

volume of sphere = (4/3)pi(12)^3 = 7238.229

(you probably got that)

now the 'cylinder will cut at (√135,3)and (-√135,3)

so the volume of the cylinder with flat tops = pi(3)^2(2(√135)) = 1642.59

( I am going to assume you got an answer of 7238.229-1642.59 = 5595.639)

I will calculate one of the "caps", then subtract twice that from the above answer.

vol. of cap = pi[integral](144-x^2)dx from √135 to 12

= pi[144x - (1/3)x^3│ from √135 to 12

= 5.4159

CHECK MY ARITHMETIC, THIS IS WHERE I USUALLY SCREW UP

so total volume

= 7238.229 - 1642.59 - 2(5.4159

= 5584.8072

- silly arithmetic error Calculus -
**Reiny**, Monday, April 27, 2009 at 6:04pmARRGGGHH! ARITHMETIC ERROR!!

<< so the volume of the cylinder with flat tops = pi(3)^2(2(√135)) = 1642.59 >>

should have said:

so the volume of the cylinder with flat tops = pi(3)^2(2(√135)) = 657.036

and then

<<( I am going to assume you got an answer of 7238.229-1642.59 = 5595.639) >>

should say:

( I am going to assume you got an answer of 7238.229-657.036 = 6581.19

and finally at the end

<< so total volume

= 7238.229 - 1642.59 - 2(5.4159

= 5584.8072 >>

should say:

so total volume

= 7238.229 - 657.036 - 2(5.4159

= 6570.36

**Related Questions**

calculus 2 - A ball of radius 12 has a round hole of radius 6 drilled through ...

Calculus - A ball of radius 14 has a round hole of radius 8 drilled through its ...

calculus - A ball of radius 10 has a round hole of radius 8 drilled through its ...

Calculus - A ball of radius 16 has a round hole of radius 4 drilled through its ...

calculus - A ball of radius 10 has a round hole of radius 5 drilled through its ...

calculus - Find the volume that remains after a hole of radius 1 is bored ...

physics - A curcial part of a piece of machinery starts as a flat uniform ...

Physic - A machine part is made from a uniform solid disk of radius R = 0.161 m ...

Physics - A machine part is made from a uniform solid disk of radius R and mass ...

science - If we drilled a hole straight through the earth, and dropped a golf ...