1496 , cm^3 of a metal is used to cast a pipe | vedclass

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(B) Let the outer radius be $R \, cm$ and the internal radius be $r = 8 \, cm$. The length (height) of the pipe is $h = 28 \, cm$.The volume of the me

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) Let the outer radius be $R \, cm$ and the internal radius be $r = 8 \, cm$. The length (height) of the pipe is $h = 28 \, cm$.The volume of the metal used to cast the pipe is given by the formula for the volume of a hollow cylinder:$V = \pi h (R^2 - r^2)$Given $V = 1496 \, cm^3$,$h = 28 \, cm$,and $r = 8 \, cm$,we have:$1496 = \frac{22}{7} 	imes 28 	imes (R^2 - 8^2)$$1496 = 22 	imes 4 	imes (R^2 - 64)$$1496 = 88 	imes (R^2 - 64)$$R^2 - 64 = \frac{1496}{88}$$R^2 - 64 = 17$$R^2 = 17 + 64 = 81$$R = \sqrt{81} = 9 \, cm$.Thus,the outer radius of the pipe is $9 \, cm$.

$1496 \, cm^3$ of a metal is used to cast a pipe of length $28 \, cm$. If the internal radius of the pipe is $8 \, cm$,then the outer radius of the pipe is (in $cm$):

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