The radius of a cylinder is 10, cm and its he | vedclass

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(A) Let the radius be $r = 10\, cm$ and the height be $h = 4\, cm$.Let the value added to either the radius or the height be $x\, cm$.Case $1$: When $

Vedclass · Accepted Answer

$5$

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(A) Let the radius be $r = 10\, cm$ and the height be $h = 4\, cm$.Let the value added to either the radius or the height be $x\, cm$.Case $1$: When $x$ is added to the radius,the new radius is $(10+x)\, cm$ and the height remains $4\, cm$.The new volume $V_1 = \pi(10+x)^2 	imes 4$.Case $2$: When $x$ is added to the height,the radius remains $10\, cm$ and the new height is $(4+x)\, cm$.The new volume $V_2 = \pi(10)^2 	imes (4+x)$.According to the problem,the increase in volume is the same,which implies $V_1 = V_2$ (since the original volume is subtracted from both sides,the net increase is equal if the final volumes are equal).$\pi(10+x)^2 	imes 4 = \pi(10)^2(4+x)$$(10+x)^2 	imes 4 = 100(4+x)$$4(100 + 20x + x^2) = 400 + 100x$$400 + 80x + 4x^2 = 400 + 100x$$4x^2 - 20x = 0$$4x(x - 5) = 0$Since $x$ cannot be $0$,we have $x = 5\, cm$.

The radius of a cylinder is $10\, cm$ and its height is $4\, cm$. The value of $x$ (in $cm$) that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is:

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