1.

The volume of a metallic cylindrical pipe is `784 cm^(3)`. Its length is 14 cm and its external radius is 9 cm. Find its thickness

Answer» Volume of the pipe, `V = 748 cm^(3)`. Length of the pipe, `h = 14 cm`
External radius of the pipe, R = 9cm
Let the internal radius of the pipe be r cm. Then,
volume of the pipe `= (pi R^(2) h = pi r^(2)h)`
`= {pi (R^(2) - r^(2)) h} cm^(3)`
`= {(22)/(7) xx (81 - r^(2)) xx 14} cm^(3)`
But, volume of the pipe = `748 cm^(3)`
`:. (22)/(7) xx (81 - r^(2)) xx 14 = 748`
`rArr 44 xx (81 - r^(2)) = 748`
`rArr (81 - r^(2)) = (748)/(44) = 17 rArr r^(2) = (81 - 17) = 64 = 8^(2)`
`rArr r = 8cm`
`:.` thickness `= (R -r) cm = (9 - 8) cm = 1 cm`


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