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Question
Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are metled and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.
Solution
For cylinder 1,
Height = h1 = 30 cm
Radius = r1 = `60/2` = 30 cm
Volume = V1
= `pir_1^2h_1`
= π × 30 × 30 × 30
= 27000π cm3
For cylinder 2,
Height = h2 = 60 cm
Radius = r2 = 30 cm
Volume = V2
= `pi "r"_2^2 "h"_2`
= π × 30 × 30 × 60
= 54000π cm3
Let r be the radius of the third cylinder.
Height = h = 10 cm
Volume = V
= πr2h
= πr2 × 10
Now,
V = V1 + V2
`=>` πr2 × 10 = 27000π + 54000π
`=>` πr2 × 10 = 81000π
`=>` r2 = 8100
`=>` r = 90
`=>` Diameter = 2r = 180 cm
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