a) A cylinder has a radius of 0.25±0.2 cm and a height of 0.52±0.3cm. Find the...

Question

Question

a) A cylinder has a radius of 0.25±0.2 cm and a height of 0.52±0.3cm. Find the volume of the cylinder and its absolute error.

b)Given that x = 5.00±0.02cm, y=8.00±0.04cm. Find the value of ? = ? 8 + 5? and its percent error and absolute error.

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Answer 1

Answer #1

a] Volume V = pi*r^2*h = pi*0.25^2*0.52 = 0.10 cm^3

For error dV/V = 2*dr/r + dh/h

dV/0.102 = 2*0.2/0.25 + 0.3/0.52

dV = 0.102*[2.177] = 0.22 cm^3

volume is 0.102 cm^3 and error is 0.222 cm^3

Note error is very high because data given has unbelievably high error 0.25+/- 0.2 cm, it should have been 0.25+/- 0.02 cm

b] z= x^8 +5y = 5^8 +5*8 = 390665

error dz/z = 8*dx/x

dz/z = 8*0.02/5 = 0.032

percentage error = 0.032*100 = 3.2 % answer

absolute error = z*0.032 = 390665*0.032 = 12501

Answer 2

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