I read it as a round whole not a spherical hole. So think a drillbit of radius 4 straight through the center of the sphere. The sphere has a volume of .
The cylindrical portion of the hole has a radius of 4 but what is the height? Draw a circle of radius 14 and inscribe in it a rectangle whose top and bottom have length 8 (a crossection of the sphere through a great circle "parallel" to the hole). Draw a radius to a point on the rectangle and and the circle (the corner of the rectanlge), and draw a vertical radius. Now you have a right trangle whose hypotenuse is length 14 and whose base is length 4.
Therefore the height of the cylinder is .
So the volume of this cylinder is
What tools do you have for calculating volume. Do you have integral calculus?
I must assume that this is a Calculus problem.
A ball of radius 14 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.Code:14| * * * *:::::|:::::* *:::::::|:::::::* *--------+--------* 4| * | * - - * - - - - + - - - - * - - * | * | *- - - - + - - - -* * | * * | * * * * |
We have a circle: .
We have the region bounded by the upper semicircle and
Revolve it about the x-axis to generate the desired solid.
The circle and horizontal line intersect at:
The volume of the solid is: .
And we have: .
I get: .