A right circular cylinder and a cone are there. Base radius of cone is equal to radius of cylinder. What is the ratio of height to slant side
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Volume of a cylinder = (pi)r^2*h(cylinder).
Volume of a cone = (1/3)(pi)r^2*h(cone).
Since volumes are the same, h(cylinder)= (1/3)(cone, or
h(cone) = 3h(cylinder).
Slant height of cone = [r^2 + h(cone)^2]^0.5 = [1 + h(cone)^2]^0.5
= [1 + {3h(cylinder)}^2]^0.5
Hence, ratio of height of cylinder to slant height of cone =h(cylinder) : [1 + {3h(cylinder)}^2]^0.5 .
If h(cylinder) is taken as unity, then ratio of height of cylinder to slant height of cone =1 : [1 + 3^2]^0.5 = 1:√10.
Volume of a cone = (1/3)(pi)r^2*h(cone).
Since volumes are the same, h(cylinder)= (1/3)(cone, or
h(cone) = 3h(cylinder).
Slant height of cone = [r^2 + h(cone)^2]^0.5 = [1 + h(cone)^2]^0.5
= [1 + {3h(cylinder)}^2]^0.5
Hence, ratio of height of cylinder to slant height of cone =h(cylinder) : [1 + {3h(cylinder)}^2]^0.5 .
If h(cylinder) is taken as unity, then ratio of height of cylinder to slant height of cone =1 : [1 + 3^2]^0.5 = 1:√10.
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