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What Length of a Solid Cylinder 2 Cm in Diameter Must Be Taken to Recast into a Hollow Cylinder of Length 16 Cm, External Diameter 20 Cm and Thickness 2.5 Mm? - Mathematics

Sum

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

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Solution

Here, r = Internal radius
        R = External radius = 10 cm
        h = Length of the cylinder
        t = Thickness = 0.25 cm
Volume of the hollow cylinder = πh(R2 - r2) = π (16) (102 - (10-0.25)2) = 79 π cm3
Volume of the solid cylinder = Volume of the hollow cylinder
We know that the radius of the solid cylinder is 1 cm.
∴ π(12)h = 79 π​
h = 79 cm
Hence, length of the solid cylinder that gives the same volume as the hollow cylinder is 79 cm.

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 22 Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)
Exercise 22.2 | Q 42 | Page 27
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