Question

A right circular solid cone of base radius 42cm and height 84cm has the same volume as a solid cylinder of height 112cm find the radius of the cylinder

Answer 1

Answer:

21 cm

Step-by-step explanation:

Volume of cone is given by $1/3(\pi r^2h)$

volume of cylinder is given by $\pi r^2h$

where r is the radius of base and h is the height

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For cone

radius = 42cm

height = 84

volume = $1/3(\pi *42^2*84)$  (1)

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For cone

radius = to find let it be r

height =112

volume = $\pi *r^2*112$  (2)

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since , volume of both solid are same

thus, equation 1 = equation 2

$1/3(\pi *42^2*84) = \pi *r^2*112\\=> r^2 = 1/3((\pi *42^2*84) / 112*\pi \\=> r^2 = 1/3(42*42*84/112) = 441\\=> r = \sqrt{441} \\=> r = 21$

Thus, radius of cylinder is 21 cm