The volume of a cylinder is found using the formula V=piR^2h , where R is the radius of the base and h is the height. The volume of a rectangular prism of the same width (2r) and height h, as the cylinder, is found by multiplying the area of the base (2r*2r) by the height. What is the ratio of the volume of the cylinder to the volume of the prism?
The volume of a cylinder is
Vc=pi r^2 h
The volume of a rectangular prism is
Vp= 4 r^2 h
The ratio of the volume of the cylinder to the volume of the prism
Vc / Vp = (pi r^2 h) / (4 r^2 h) = pi /4 = 0.25 pi =0.785
The ratio of the volume of the cylinder to the volume of the rectangular prism is 0.785.
Suppose that the radius of the considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
\(V = \pi r^2 h \: \rm unit^3\)
The volume of a rectangular prism is
Vp = 4 x r^2 x h
The ratio of the volume are
Vc / Vp = (π x r^2 x h) / (4 x r^2 x h)
= π /4
= 0.25 π
= 0.785
The ratio of the volume of the cylinder to the volume of the rectangular prism is 0.785.
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