Madhur wants to make a model of a traffic light signal. He used a cardboard of length 60 cm and breadth 15 cm. Three circles each of radius 7 cm are to be pasted on it. Find the area of the cardboard, which is not covered by the circles ?

Dear Student,

$$\begin{gathered} \mathrm{Given} \mathrm{length} \mathrm{of} \mathrm{cardboard}, \mathrm{l}=60 \mathrm{cm} \\ \mathrm{And}, \mathrm{breadth}, \mathrm{b}=15 \mathrm{cm} \\ \mathrm{So}, \\ \mathrm{Area} \mathrm{of} \mathrm{cardboard}=\mathrm{l}\times \mathrm{b}=60\times 15=900 {\mathrm{cm}}^2 \\ \Rightarrow \mathrm{Area} \mathrm{of} \mathrm{cardboard}=900 {\mathrm{cm}}^2 \\ \mathrm{And}, \\ \mathrm{Radius} \mathrm{of} \mathrm{circle},\mathrm{r}=7 \mathrm{cm} \\ \mathrm{So}, \\ \mathrm{Area} \mathrm{of} \mathrm{circle}={\mathrm{\pi r}}^2 \\ =\frac{22}{7}\times {\left(7\right)}^2 \\ =22\times 7 \\ =154 {\mathrm{cm}}^2 \\ \Rightarrow \mathrm{Area} \mathrm{of} \mathrm{three} \mathrm{circles}=3\times 154=462 {\mathrm{cm}}^2 \\ \mathrm{According} \mathrm{to} \mathrm{question}: \\ \mathrm{Area} \mathrm{of} \mathrm{cardboard} \mathrm{which} \mathrm{is} \mathrm{not} \mathrm{covered} \mathrm{by} \mathrm{circles}=\left(\mathrm{Area} \mathrm{of} \mathrm{cardboard}\right)-\left(\mathrm{Area} \mathrm{of} \mathrm{three} \mathrm{circles}\right) \\ =900-462 \\ =438 {\mathrm{cm}}^2 \\ \mathrm{Hence}, \mathrm{area} \mathrm{of} \mathrm{cardboard} \mathrm{which} \mathrm{is} \mathrm{not} \mathrm{covered} \mathrm{by} \mathrm{circles} \mathrm{is} 438 {\mathrm{cm}}^2. \end{gathered}$$

Hope this information will clear your doubts about the topic.                                                                                            

If you have any more doubts, just ask here on the forum and our expert will try to help you out as soon as possible.                                                                                                      

Regards