question_answer 26)

From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in adjoining figure). Find the area of the remaining sheet. \[\left( \text{Take  }\!\!\pi\!\!\text{  = }\frac{\text{22}}{\text{7}} \right)\]

Answer:

                Radius of the circular card sheet (r) = 14 cm \[\therefore \] Area of the circular card sheet       \[=\pi {{r}^{2}}=\frac{22}{7}{{(14)}^{2}}\] \[\text{= }\frac{\text{22}}{\text{7}}\text{  }\!\!\times\!\!\text{  14  }\!\!\times\!\!\text{  14 = 616 c}{{\text{m}}^{\text{2}}}\] Area of two circles of radius 3.5 cm      \[\text{=2 }\!\![\!\!\text{ }\pi {{(3.5)}^{2}}\text{ }\!\!]\!\!\text{  c}{{\text{m}}^{2}}\] \[=2\left[ \frac{22}{7}\times 3.5\times 3.5 \right]\text{c}{{\text{m}}^{\text{2}}}=\text{77c}{{\text{m}}^{\text{2}}}\] Area of a rectangle of length 3 cm and breadth 1 cm \[=l\times b=3\times \text{1 c}{{\text{m}}^{\text{2}}}=\text{3 c}{{\text{m}}^{\text{2}}}\] \[\therefore \] Area of the remaining sheet \[=\text{616 c}{{\text{m}}^{\text{2}}}-(\text{77 c}{{\text{m}}^{\text{2}}}+\text{3 c}{{\text{m}}^{\text{2}}})\] \[=\text{616 c}{{\text{m}}^{\text{2}}}-\text{8}0\text{ c}{{\text{m}}^{\text{2}}}=\text{536 c}{{\text{m}}^{\text{2}}}.\]