A hemisphere fits snugly inside a cylinder with a radius of 12 cm. A cone fits snugly inside the same hemisphere. What is the volume of the cylinder in terms of LaTeX: \piπ? Show all work.

The volume of the cylinder is 1,728·π cm³

Step-by-step explanation:

The given parameters are;

The radius of the cylinder, r = 12 cm

The location of the hemisphere = Inside the cylinder

The size relationship between the hemisphere and the cone = Snuggly fit

Therefore, we have;

The radius of the hemisphere = The radius of the cylinder = 12 cm

The height of the cylinder, h = The radius of the hemisphere = 12 cm

The volume of the cylinder, V = π·r²·h

Where;

h = 12 cm

r = 12 cm

Therefore;

V = π·r²·h = π × (12 cm)² × 12 cm = (12 cm)³·π = 1,728·π cm³

The volume of the cylinder, V, in terms of pi (π) is, V = 1,728·π cm³.

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