Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is drilled through the center of the hemisphere perpendicular to its base.

Step-by-step explanation:

Inicially we have to separate the sphere into 3 parts:

The donut  +  1 ball cap (or a dome) +  the cylinder hole = the Hemisphere

vide picture

As it shows in the picture we have to find the donut.

The donut  = the Hemisphere - ( 1 dome +  the cylinder hole)

By basic algebra we have

D = 5.304

*The dome in the 1st picture is represented by the color orange.Looking into the second picture, the dome formula derivatives from the volume of a dome of a hemisphere. By using the following linear system:

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

8 2/3 is the answer

step-by-step explanation: just use a calculator