Question

Find the perimeter of the steel plate shown in the figure. Be sure to take into account allcircular cuts made.7"2"radiusradius10"-8"

Answer 1

To find the perimeter of the given steel plate:

1. Find the circular lengths; use the formula of the circumference of a circle and divide it in to 4 to find the length of those parts (those parts are quarter of circle):

Quarter circle part with radius 2"

$\begin{gathered} C=2\pi r \\ C=2\pi(2") \\ C=4\pi \\ \\ Divide\text{ into 4:} \\ \frac{4\pi}{4}=\pi \end{gathered}$

Quarter circle part with radius 1"

$\begin{gathered} C=2\pi(1") \\ C=2\pi \\ \\ Divide\text{ into 4:} \\ \frac{2\pi}{4}=\frac{1}{2}\pi \end{gathered}$

2. Add the lengths of each side of the plate to find its perimeter:

$\begin{gathered} P=10"+7"+7"+6"+\pi"+\frac{1}{2}\pi" \\ \\ P=30"+\frac{3}{2}\pi" \\ \\ P\approx34.71" \end{gathered}$Then, the perimeter of the plate is:Exact answer: 30"+3/2 π"Approximate answer: 34.71"