# calculus

posted by .

Find the volume that remains after a hole of radius 1 is bored through the center of a solid sphere of radius 2.

• calculus -

A little investigation will lead you to the formula that if a hole of radius r is drilled through a sphere of radius R, the remaining volume is just 4pi/3 (R^2 - r^2)^(3/2)

In this case, that would be 4pi/3 * 3√3 = 4√3 pi
__________________________

You might also look up the napkin ring problem, where it is shown that if a hole of length h is drilled through a sphere, the remaining volume is independent of the radius of the sphere!

In this case, h/2 = R^2 - r^2 = √3, so h = 2√3

The remaining volume is pi/6 h^3 = pi/6 * 24√3 = 4√3 pi

• calculus -

thanks!

## Similar Questions

1. ### calculus

A ball of radius 10 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid.
2. ### Calculus

A ball of radius 16 has a round hole of radius 4 drilled through its center. Find the volume of the resulting solid.
3. ### calculus

A ball of radius 10 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
4. ### Calculus

A ball of radius 12 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid. I tried finding the volume of the sphere and the volume of the cyclinder then subtract however that did not work.
5. ### calculus 2

A ball of radius 12 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid.
6. ### Calculus

A ball of radius 14 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid
7. ### calculus

3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of increase …
8. ### calculus 1 (I need help)

The portion of the ellipse x^2/9+y^2/4=1 with x greater than or equals to 0 is rotated about the y-axis to form a solid S. A hole of radius 1 is drilled through the center of S, along the y-axis. Find the exact volume of the part of …
9. ### Calculus Help

Suppose you drill a circular hole with radius r through the center of a sphere with radius R. You remove exactly half the volume of the sphere. The ratio of your radii is: r/R=
10. ### Calculus

Imagine slicing through a sphere with a plane (sheet of paper). the smaller piece produced is called a radius of the sphere. Its volume is V=(pi)h^2(3r-h)/3, where r is the radius of the sphere and h is the thickness of the cap. find …

More Similar Questions