**Center Drilled**

**A ball of radius 17 has a round hole of radius 8 drilled through its center. Find the volume of the solid.?**

♥ this object looks like a bead;

the sphere and cylinder intersect, therefore section through axis of cylinder will give us 2 equations: one of sphere

y=√(R1^2 –x^2), another one

x=R2 (a vertical line), where

R1=17”, R2=8”;

axis of rotation being y-axis!

♠ thus we get 2 intersection points

A=(8, -√(17^2 –8^2)), and B=(8, +15);

♣ y1=-15 and y2=+15 are limits of integration;

slicing the bead horizontally we get that

volume of elementary washer is

dv = dy*pi*x^2 – dy*pi*R2^2, where x=√(R1^2 –y^2);

dv = pi*dy*(17^2 –y^2 –8^2) =pi*dy*(225 –y^2);

♦ V=pi* (225y –y^3/3) {y=-15 to 15} =

= 2pi*(225*15 –15^3/3) =2250*2pi = 4500*pi =14137.17 inch^3;

**USED TREE KIRA MODEL VTC30 CNC DRILL MILL CENTER**

[affmage source=”ebay” results=”15″]Center Drilled[/affmage]
[affmage source=”amazon” results=”10″]Center Drilled[/affmage]
[affmage source=”cj” results=”5″]Center Drilled[/affmage]
[affmage source=”clickbank” results=”5″]Center Drilled[/affmage]