Question : The radius of a cylinder is 10 cm and the height is 4 cm. The number of centimeters that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is:
Option 1: 5 cm
Option 2: 4 cm
Option 3: 25 cm
Option 4: 16 cm
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Correct Answer: 5 cm
Solution : The radius of a cylinder = 10 cm Height = 4 cm Let the radius be increased by $x$ cm. ⇒ Volume of cylinder = $\pi(10+x)^{2}×4$----------(i) Let height be increased by $x$ cm. ⇒ Volume of cylinder = $\pi×10^{2}×(4+x)$-------(ii) From equations (i) and (ii), $\pi(10+x)^{2}×4$ = $\pi×10^{2}×(4+x)$ ⇒ $(10+x)^{2}×4$ = $10^{2}×(4+x)$ ⇒ $(100+x^{2}+20x)×4$ = $100×(4+x)$ ⇒ $4x^{2}+80x$ = $100x$ ⇒ $4x^{2}$ = $20x$ ⇒ $x = 5$ Hence, the correct answer is 5 cm.
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