Question

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

Answer 1

if u make a diagram then the diagram shows that a cylinder of radius 1 inscribed in a sphere
of radius 2 intersects the sphere at 60 degrees.

The diagram is needed to follow the steps.
Volume of a spherical cap = πh/6(3a^2+h^2)
where h= height of cap = 2-√3 (from diagram), a = radius of cap
V (cap) = πh/6(3×1^2+√3^2) = π×(2-√3)
V (cylinder) = πr^2(2×√3) = 2π√3
V (sphere) = 4/3π(2^3) = 32/3π

Sphere - cylinder - 2 caps
32/3π - 2π√3 -2π(2-√3) = 32/3π - 2π√3 - 4π + 2π√3 = 32/3π - 4π = 32π/3-12π/3 = 20π/3

Answer 2

@CO_oLBoY so is it 32/3 pi? because thats an answer choice but 20pi/3 isnt.

Answer 3

yup i think so

Answer 4

thanks!