Question

For a wire with a circular cross section and a diameter = 3.00mm calculate the following: (m means meter. mm means millimeter. cm means centimeter.) Calculate the cross sectional area in mm2. Calculate the cross sectional area in cm2

Answer 1

Answer:

The cross sectional area in mm2 is 7.07$mm^{2}$

The cross sectional area in cm2 is 0.0707$cm^{2}$

Explanation:

The cross-sectional area (a) of the wire is given by;

a = $\pi$ x $\frac{d^{2} }{4}$

where d is the diameter of the cross section = 3.00mm

1 => To find the cross-sectional area in $mm^{2}$, substitute the value of d = 3.00mm into the equation above as follows;

a = $\pi$ x $\frac{3.00^{2} }{4}$

Taking $\pi$ to be $\frac{22}{7}$ we have;

a = $\frac{22}{7}$ x $\frac{3.00^{2} }{4}$

a = 7.07$mm^{2}$

2 => To find the cross-sectional area in $cm^{2}$, first convert the diameter in mm to cm as follows;

3.00mm = 0.3cm

Now, substitute the value of d = 0.3cm into the equation above as follows;

a = $\pi$ x $\frac{0.3^{2} }{4}$

Taking $\pi$ to be $\frac{22}{7}$ we have;

a = $\frac{22}{7}$ x $\frac{0.3^{2} }{4}$

a = 0.0707$cm^{2}$