Question

question 2
find the area of the shaded region of the following figure:
18 cm
answer:

Explanation:

Step1: Find the width of the rectangle and radius of the circles

The length of the rectangle \( l = 18\) cm. Since there are two circles of equal diameter along the length of the rectangle, the diameter of each circle \(d=\frac{18}{2}=9\) cm. The width of the rectangle \(w = d=9\) cm (equal to the diameter of the circle), and the radius of each circle \(r=\frac{d}{2}=\frac{9}{2}\) cm.

Step2: Calculate the area of the rectangle

The area of a rectangle is \(A_{rectangle}=l\times w\). Substituting \(l = 18\) cm and \(w = 9\) cm, we get \(A_{rectangle}=18\times9 = 162\) \(cm^{2}\).

Step3: Calculate the area of the two circles

The area of a circle is \(A_{circle}=\pi r^{2}\). For two circles, \(A_{two - circles}=2\times\pi r^{2}\). Substituting \(r = \frac{9}{2}\) cm and \(\pi=\frac{22}{7}\), we have \(A_{two - circles}=2\times\frac{22}{7}\times(\frac{9}{2})^{2}=\frac{22}{7}\times\frac{81}{2}=\frac{1782}{14}=127.29\) \(cm^{2}\).

Step4: Calculate the area of the shaded region

The area of the shaded region \(A = A_{rectangle}-A_{two - circles}\). Substituting the values, \(A=162 - 127.29=34.71\) \(cm^{2}\).

Answer:

\(34.71\) \(cm^{2}\)