Volume increase

Level 2

If a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each, then the volume of the solid is increased by? (in %)

(1) 1.01

(2) 2.01

(3) 3.03

(4) 1.2

If your correct option is (1), type as 1.


The answer is 3.

Arpit Sah by Arpit Sah , 22, India

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1 solution

Eduardo Petry
Dec 30, 2013

Increasing 1 % 1\% means multiplying the inicial value by 1.01 1.01 . In this case, the percentage that we're looking for can be expressed as: V f i n a l V i n i t i a l = π ∗ ( 1.01 r ) 2 ∗ ( 1.01 h ) π ∗ r 2 ∗ h = 1.030301 π ∗ r 2 ∗ h π ∗ r 2 ∗ h = 1.030301 \dfrac{V_{final}}{V_{initial}}=\dfrac{\pi*(1.01r)^{2}*(1.01h)}{\pi*r^{2}*h} = \dfrac{1.030301\pi*r^{2}*h}{\pi*r^{2}*h}=1.030301 which means the final volume is, approximately, 103.03 % 103.03\% of the inicial volume.

Hence, the volume was increased by 103.03 % − 100 % = 3.03 % 103.03\%-100\%=\boxed{3.03\%}

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