Answer:
21 cm
Step-by-step explanation:
Volume of cone is given by [tex]1/3(\pi r^2h)[/tex]
volume of cylinder is given by [tex]\pi r^2h[/tex]
where r is the radius of base and h is the height
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For cone
radius = 42cm
height = 84
volume = [tex]1/3(\pi *42^2*84)[/tex] (1)
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For cone
radius = to find let it be r
height =112
volume = [tex]\pi *r^2*112[/tex] (2)
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since , volume of both solid are same
thus, equation 1 = equation 2
[tex]1/3(\pi *42^2*84) = \pi *r^2*112\\=> r^2 = 1/3((\pi *42^2*84) / 112*\pi \\=> r^2 = 1/3(42*42*84/112) = 441\\=> r = \sqrt{441} \\=> r = 21[/tex]
Thus, radius of cylinder is 21 cm
