question_answer 1)

From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. \[\text{(Take  }\!\!\pi\!\!\text{  = 3}\text{.14)}\]

Answer:

                                                Radius of outer circle (R) = 4 cm                             \[\therefore \] Area of the outer circle \[\pi {{R}^{2}}\]                                           \[=\text{3}.\text{14(4}{{\text{)}}^{\text{2}}}\text{c}{{\text{m}}^{\text{2}}}\]                 \[=\text{3}.\text{14}\times \text{16 c}{{\text{m}}^{\text{2}}}\]                 \[=\text{5}0.\text{24 c}{{\text{m}}^{\text{2}}}.\]                 Radius of inner circle (r) \[~=\text{3 cm}\] \[\therefore \]  Area of the inner circle \[=\pi {{r}^{2}}\]                 \[\text{= 3}\text{.14  }\!\!\times\!\!\text{  (3}{{\text{)}}^{\text{2}}}\text{ c}{{\text{m}}^{\text{2}}}\]                     \[\text{= 28}\text{.26 c}{{\text{m}}^{\text{2}}}\]              \[\therefore \] Area of the remaining sheet                      = Area of the outer circle ? Area of the inner circle                 \[=\text{5}0.\text{24 c}{{\text{m}}^{\text{2}}}-\text{ 28}.\text{26 c}{{\text{m}}^{\text{2}}}\]                 \[=\text{21}.\text{92 c}{{\text{m}}^{\text{2}}}.\]