Respuesta :
Based on the premise that the sphere's radius is irrelevant, the remaining volume is 113.1 cubic inches.
Define the term solid sphere?
- A sphere has a spherical, symmetrical shape.
- It is a three-dimensional solid with equal distances between each surface point and the center.
Let the hole's final length be 2L. Let R be the sphere's radius.
Let r represent the hole's radius.
L must equal R; since L≤R. x² - y² = R²
The outcome can be visualized as a stack with annuli.
Cut a hole in the middle of the object, with the hole's axis corresponding to the x-axis, in a plane. Place the origin as the center.
The inner radius of the annulus is equal to r = √ (R² - L²) for a particular value of x.
x² - y² = R² is satisfied by the outer radius, y.
The difference between the areas of a circle for all those two radii is the area of the an annulus.
Integrate now:
∫π(R² - x²) - (R² - L²))dx = ∫ π(L² - x²))dx
= π(L²x - x³/3) Put limits -L to +L.
= 4πL³/3
We can see that this does not depends on R irrespective of the final line to assessing the integral.
Thus, the solution, which is roughly 113.1 cubic inches, is confirmed by substituting L= 3 inches, is the remaining volume of the sphere.
To know more about the solid sphere, here
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