question_answer 18)

Find the area of the following circles, given that \[\left( \text{Take  }\!\!\pi\!\!\text{  =}\frac{\text{22}}{\text{7}} \right)\]:                 (a) radius = 14 mm          (b) diameter = 49 m           (c) radius = 5 cm

Answer:

                (a) r = 14 mm \[\therefore \]                  Area of the circle \[=\pi {{r}^{2}}\]                 \[=\frac{22}{7}{{(14)}^{2}}=\frac{22}{7}\times 14\times 14=6\text{16 m}{{\text{m}}^{\text{2}}}\]                 (b) Diameter \[=\text{ 49 m}\] \[\Rightarrow \]               Radius (r) \[=\frac{49}{2}\text{m}\] \[\therefore \]  Area of the circle                 \[\text{=}\frac{22}{7}\times \frac{49}{2}\times \frac{49}{2}\text{ }{{\text{m}}^{\text{2}}}=\frac{3773}{2}\text{ }{{\text{m}}^{\text{2}}}=1886.5\text{ }{{\text{m}}^{2}}\] (c)           \[\text{r = 5 cm}\] \[\therefore \]  Area of the circle                 \[=\pi {{r}^{2}}=\frac{22}{7}{{(5)}^{2}}=\frac{22}{7}\times 5\times 5\]                 \[=\frac{550}{7}\text{ c}{{\text{m}}^{\text{2}}}\].