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Question
A hollow metallic cylinder whose external radius is 4.3 cm and internal radius is 1.1 cm and the whole length is 4 cm is melted and recast into a solid cylinder of 12 cm long. Find the diameter of a solid cylinder
Solution
External radius of the hollow cylinder R = 4.3 cm
Internal radius of the hollow cylinder r = 1.1 cm
Length of the cylinder (h) = 4 cm
Length of the solid cylinder (H) = 12 cm
Let the radius of the solid cylinder be x
Volume of the solid cylinder = Volume of the hollow cylinder
πr2H = πh(R2 − r2)
x2 × 12 = 4(4.32 − 1.12)
12x2 = 4 × 5.4 × 3.2
12x2 = 4(4.3 + 1.1) (4.3 − 1.1)
x2 = `(4 xx 5.4 xx 3.2)/12`
= `(4 xx 54 xx 32)/(12 xx 100)`
= `(54 xx 32)/(3 xx 100)`
= `(18 xx 32)/100`
x = `sqrt((18 xx 32)/100)`
= `sqrt((2 xx 9 xx 2 xx 16)/100)`
= `(2 xx 3 xx 4)/10`
= 2.4 cm
Diameter of the solid cylinder
= 2 × 2.4
= 4.8 cm
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