Suppose a cylinder has a height and diameter which are equal (d=h=2.000cm). Calc

Question

Suppose a cylinder has a height and diameter which are equal (d=h=2.000cm). Calculate the actual volume V of the cylinder. Now, consider two other cases: what happens to V when h is measured correctly but d is measured 10% too high, and then what happens to V when d is correct but h is measured 10% too high. Show your work below.

V= actual V= (if 10% error in d) V= (if 10% error in h)

An error in which dimension (d or h) has the largest effect on the accuracy in the volume V? Explain why by analyzing the formula for the volume of a cylinder.

Explanation / Answer

Actual Volume of a cylinder=V=r2h=× (2/2)2× 2=2 cm3 =6.28 cm3

if the diameter is 10 percent high then d=2+(2×10/100)=2.2 cm

Radius=2.2/2=1.1cm

Volume of cylinder=V1=r2h=× (1.1)2× 2=2.42 cm3 = 7.6 cm3

if the height is 10 percent high then h=2+(2×10/100)=2.2 cm

radius=2/2=1cm

Volume of cylinder=V2=r2h=× (1)2× 2.2=2.42 cm3 = 2.2 cm3=6.91 cm3

As Volume of cylinder is r2h.

Volume directly varies with square of radius and height.So if radius is increased by 10 percent then volume will increase more than when height increased by 10 percent.

V1>V2>V

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