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:$28.61 cm^2$

Explanation:

Given

radius $r=\frac{d}{2}=3 cm$

length L= 3 cm

$\frac{\delta r}{r}=0.006$

$\delta r=0.006\times r$

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

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

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

$A'=\pi\times 9.108$

$A'=28.61 cm^2$