Question

A cylindrical rod initially has length 3.0 meters and diameter 6.0 cm. Due to thermal expansion, this bar expands by the same fractional amount in each direction. Specifically, \frac{\Delta r}{r}=Δ r r = 0.006 . The cross sectional area A of a cylinder is given by: A=\pi\:r^2\:A = π r 2, where rr is the radius of the cylinder. What is the cross sectional area (in inches2 ) of this cylinder after the expansion has occurred ?

Answer 1

Answer:
`28.61 cm^2`

Step-by-step explanation:

Given

radius
`r=(d)/(2)=3 cm`

length L= 3 cm

`(\delta r)/(r)=0.006`

`\delta r=0.006* r`

New radius
`r'=r+\delta r=3+0.018=3.018 cm`

New Area
`A'=\pi (r')^2`

`A'=\pi (3.018)^2`

`A'=\pi* 9.108`

`A'=28.61 cm^2`