SOLUTION: A cylindrical mettalic pipe is 21cm long.The difference between outside and inside surface area is 44 cm². If the pipe is made up of 110 cm of metal. Find the inner and outer diame

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Question 1069067: A cylindrical mettalic pipe is 21cm long.The difference between outside and inside surface area is 44 cm². If the pipe is made up of 110 cm of metal. Find the inner and outer diameter of pipe.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for outside surface area is
+2%2Api%2Ar%2Ah+=+2%2Api%2Ar%2A21+
+2%2Api%2Ar%2Ah+=+42%2Api%2Ar%5B1%5D+
The inside surface area is:
+2%2Api%2Ar%5B2%5D%2A21+=+42%2Api%2Ar%5B2%5D+
-------------------------------
The difference of the surface areas is equal to
(1) +42%2Api%2A%28+r%5B1%5D+-+r%5B2%5D+%29+=+44+ cm2
--------------------------------------------
The volume of the metal is
[ vol of outside cylinder ] minus [ vol of the hollow part ]

You are given that:
(2) +21%2Api%2A%28+r%5B1%5D%5E2+-+r%5B2%5D%5E2+%29+=+110+ cm3
------------------------------------------
(1) +r%5B1%5D+-+r%5B2%5D+=+44+%2F+%28+42%2Api+%29+
(1) +r%5B1%5D+-+r%5B2%5D+=+.3335+
(1) +r%5B1%5D+=+r%5B2%5D+%2B+.3335+
and
(2) +r%5B1%5D%5E2+-+r%5B2%5D%5E2+=+110+%2F+%28+21%2Api+%29+
(2) ++r%5B1%5D%5E2+-+r%5B2%5D%5E2+=+1.6673+
(2) ++%28+r%5B2%5D+%2B+.3335+%29%5E2+-+r%5B2%5D%5E2+=+1.6673+
(2) +r%5B2%5D%5E2+%2B+.667r%5B2%5D+%2B+.1112+-+r%5B2%5D%5E2+=+1.6673+
(2) ++.667r%5B2%5D+%2B+.1112+=+1.6673+
(2) +.667r%5B2%5D+=+1.5561+
(2) +r%5B2%5D+=+2.333+
and
(1) +r%5B1%5D+=+r%5B2%5D+%2B+.3335+
(1) +r%5B1%5D+=+2.333+%2B+.3335+
(1) +r%5B1%5D+=+2.6665+
------------------------------------------
Outside diameter =
+2%2Ar%5B1%5D+=+2%2A2.6665+
+2%2Ar%5B1%5D+=+5.333+ cm
Inside diameter =
+2%2Ar%5B2%5D+=+2%2A2.333+
+2%2Ar%5B2%5D+=+4.666+ cm
--------------------------
check answers:
(1) +42%2Api%2A%28+r%5B1%5D+-+r%5B2%5D+%29+=+44+
(1) +42%2Api%2A%28+2.6665+-+2.333+%29+=+44+
(1) +42%2Api%2A.3335+=+44+
(1) +131.947%2A.3335+=+44+
(1) +44.004+=+44+
close enough
(2) +21%2Api%2A%28+r%5B1%5D%5E2+-+r%5B2%5D%5E2+%29+=+110+
(2) +21%2Api%2A%28+2.6665%5E2+-+2.333%5E2+%29+=+110+
(2) +21%2Api%2A%28+7.1102+-+5.4429+%29+=+110+
(2) +21%2Api%2A1.6673+=+110+
(2) +65.9734%2A1.6673+=+110+
(2) +109.998+=+110+
close enough