Question

From a circular sheet of radius $4\mathrm{cm}$, a circle of radius $3\mathrm{cm}$ is removed. Find the area of the remaining sheet. (Take $\mathrm{\pi }=3.14$)

Answer 1

Step 1: Calculate the area of the circular sheet

Area of a circle is given as, $\mathrm{area}=\mathrm{\pi }{r}^2$

Radius of the circular sheet, $r_1=4\mathrm{cm}$

Thus, the area of the circular sheet,

$$\begin{gathered} A_1=\mathrm{\pi }\times 4^2 \\ =3.14\times 4^2 \\ =50.24{\mathrm{cm}}^2 \end{gathered}$$

Step 2: Calculate the area of the removed circle

Radius of the removed circle, $r_2=3\mathrm{cm}$

Thus, the area of the circular sheet,

$$\begin{gathered} A_2=\mathrm{\pi }\times 3^2 \\ =3.14\times 3^2 \\ =28.26{\mathrm{cm}}^2 \end{gathered}$$

Step 3: Calculate the area of the remaining sheet

Area of the remaining sheet, $A=A_1-A_2$

Thus,

$$\begin{gathered} A=50.24-28.26 \\ =21.98{\mathrm{cm}}^2 \end{gathered}$$

Therefore, the area of the remaining sheet is $21.98{\mathrm{cm}}^2$.