Answer:
V₂ = V₁
Step-by-step explanation:
Let the height of the rectangular prism = h
Let <em>s</em> represent the side length of the base of the square prism, we have;
The volume of the prism, = s²·h
The volume of the square pyramid, = (1/3)·s²·h
∴ V₁ = The area not taken up by the square pyramid = -
∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h
Similarly, for the cylinder, we have;
Let <em>h</em> represent the height of the cylinder
Let <em>r</em> represent the radius of the base of the cone, we have;
Therefore;
The volume of the cylinder, = π·r²·h
The volume of the cone, = (1/3)·π·r²·h
∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h
V₂ = (2/3)·π·r²·h
=
Therefore;
(1/3)·π·r²·h = (1/3)·s²·h
∴ π·r² = s²
Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁
V₂ = V₁.