# Center Drilled

11 years ago

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;

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