Question

12. The radius of a spherical hot-air balloon is measured as 20 feet with a possible error of 2 feet. 4 vaar a. Use differentials to calculate the maximum error in the estimate of the volume. b. What is the percent error in computing the volume of the balloon to the nearest hundredth of a percent?

Answer 1

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ANSWER - given that r = 20feet, error = Ar = 0.2 feet Now, volume is given by 4 V 3rr3 taking "In" both sides In V = In InV = ln T +In(13) 3 4 In V = In ET + 3 ln(r) 3 on differentiating both sides, Basic rules(1)In(ab) = In(a) + In(b) (2)In(a) = ln(b) on differentiating both sides, we get Δα Ab b (3)Aa = 0 if a = constant а AV - 0 + 3 V Ar SAV = 3 V 4 Tr Ar AV = 3 → AV = 41 r2 (Ar) maximum error in volume = AV = 1005.31 AV % error in computing the volume -*100 % V 1005.31 -*100 % = 4 37(20)3 = 3 % % error in computing the volume = 3 % #ANS....