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CBSE Class 9 Answered

A hollow cylindrical metal pipe is 80 cm long. Its internal and external radii are 8 cm and 10 cm respectively. It is melted and cast into a solid cylinder 20 cm long. Calculate the radius of the solid cylinder.
Asked by Topperlearning User | 13 Oct, 2017, 02:08: PM
answered-by-expert Expert Answer

Given: Internal radius (r) =8 cm

External radius (R) = 10 cm

Length of the cylindrical tube (h) = 80 cm

Let V denote the volume of metal in the tube.

                        begin mathsize 12px style straight V space equals space straight pi open parentheses straight R squared space minus space straight r squared close parentheses straight h straight V space equals space 22 over 7 cross times open square brackets 10 squared space minus space 8 squared close square brackets cross times 80 space straight V space equals space 63360 over 7 space cm cubed end style

            Thus, volume of metal in the pipe is begin mathsize 12px style 63360 over 7 space cm cubed end style

It is melted and recasted into a cylinder. Length of the cylinder (H) = 20 cm.

Let R1 be the radius of the recasted cylinder and V1 denote its volume. Then,

V subscript 1 equals 63360 over 7 c m cubed rightwards double arrow straight pi left parenthesis straight R subscript 1 right parenthesis squared straight H equals 63360 over 7 straight c straight m cubed rightwards double arrow left parenthesis straight R subscript 1 right parenthesis squared equals fraction numerator 63360 cross times 7 over denominator 22 cross times 20 cross times 7 end fraction straight c straight m cubed equals 144 space cm cubed rightwards double arrow straight R subscript 1 equals 12 space cm

Thus, radius of the solid cylinder is 12 cm.

Answered by | 13 Oct, 2017, 04:08: PM

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