Question

The radius of a 10 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.1 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer.

Answer 1

Explanation:

Given that a cylinder has radius equal to 10 inches but measured to be 4 inches

The margin of error is +1 or -1 meaning that

the radius can take values between 3.9 and 4.1 inches

Volume of cylinder =
`\pir^(2) h\\=100\pih`

where h is height

The above is the actual volume.

Measured volume would be between radius 3.9 and 4.1 inches

i.e. Measured volume =
`\pi(3.9)^2 h <V<\pi4.1^2h\\15.21\pi h<V<16.81\pi h`

Volume would be between these two values

Possible error =100-15.21 = 84.79 pi h

OR = 84.19 pi h cubic inches