The radius and height of a cone are measured as 6 cm and 12 cm respectively and there is an error of 0.06 cm in both the measurements. The approximate error in the volume of the cone is

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$60 π$ cubic cm

$410 π \sqrt{2}$ cubic cm

$320 π \sqrt{2}$ cubic cm

$3.6 π$ cubic cm

answer is C.

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Detailed Solution

$r = 6 h = 12 δ r = δ h = 0.06 V = \frac{1}{3} π r^{2} h \Rightarrow δ r = \frac{1}{3} π (r^{2} δ h + 2 rh δ r) = \frac{π}{3} (36 + 144) \times 0.06 = π (180) (0.02) = 3.6 π$

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