The volume of the ring-shaped solid that remains after drilling is 3961.73cm³.
The radius of the cylindrical drill is 5cm and the radius of the sphere is found to be 10cm.
After drilling,
The radius of the of the sphere will act as a hypotenuse to the triangle where the base is the radius of the cylinder and the perpendicular is the height of the cylinder.
So, we can say,
Height H of cylinder = √(10² - 5²)
Height H of cylinder = 8.66 cm.
The volume V of the ring shape remaining,
V = Volume of sphere - volume of cylinder
V = 4/3πR³ - 1/3πr²H
R is the radius of sphere and r is the radius of cylinder,
Putting values,
V = 4/3π(10)³ - 1/3π(5)²8.66
V = 3961.73 cm³.
So, the volume that remains is 3961.73cm³.
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