A cylindrical container has its height twice the radius of the base. If due to imperfection in measuring callipers, 1 cm is taken as 1.02 cm, the percentage error in the volume is

<p>Let h = height of the container, </p><p>Given, h = 2r</p><p><math><mrow><mo>∴</mo></mrow></math>&nbsp;Volume v = πr²h = πr² (2r) = 2πr³</p><p><math><mrow><mo>∴</mo></mrow></math>&nbsp;Absolute error = (1.02)³ × 2πr³ − 2πr³ × 13</p><p>= 2πr³ [ (1.02)² − 1] = 2πr³ [1.0612 − 1]</p><p>= 0.0612 × 2πr³</p><p><math><mrow><mo>∴</mo></mrow></math>&nbsp;% error&nbsp;<math><mrow><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0</mn><mn>6</mn><mn>1</mn><mn>2</mn><mo>×</mo><mn>2</mn><mi>π</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>π</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mfrac><mo>×</mo><mn>1</mn><mn>0</mn><mn>0</mn><mn>%</mn><mo>=</mo><mn>6</mn><mo>.</mo><mn>1</mn><mn>2</mn><mn>%</mn></mrow></math></p>

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