Chapter 15, Problem 18CR

(a)

To determine

To Find: The area of the shaded region.

Answer to Problem 18CR

  $188.4unit{s}^2$

Explanation of Solution

Given:

  

Formula Used:

  $Area=\pi r^2$

Calculation:

  $\begin{array}{l}\text{As per given figure}\\ \text{Diameter of bigger semi-circle}=6+4+6=16\\ R=\frac{D}{2}=\frac{16}{2}=8\\ \text{Diameter of smaller semi-circle}=4\\ r=\frac{d}{2}=\frac{4}{2}=2\\ \text{Area of shaded region }=\pi R^2-\pi r^2\\ \text{⇒}A=\pi \left(8^2-2^2\right)\\ \text{⇒}A=3.14\times 60\\ \text{⇒}A=188.4unit{s}^2\end{array}$

Conclusion:

Thus the required area is $188.4unit{s}^2$ .

(b)

To determine

To Find: The perimeter of the given figure.

Answer to Problem 18CR

  $37.68units$

Explanation of Solution

Given:

  

Formula Used:

  $Perimeter=2\pi r$

Calculation:

  $\begin{array}{l}\text{As per given figure}\\ \text{Diameter of bigger semi-circle}=6+4+6=16\\ R=\frac{D}{2}=\frac{16}{2}=8\\ \text{Diameter of smaller semi-circle}=4\\ r=\frac{d}{2}=\frac{4}{2}=2\\ Perimeter=2\pi R-2\pi r\\ \text{⇒}P=2\pi \left(8-2\right)\\ \text{⇒}P=2\times 3.14\times 6\\ \text{⇒}P=37.68units\end{array}$

Conclusion:

Thus the required perimeter is $37.68units$ .