question_answer 27)

A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? \[\left( \text{Take }\pi =\text{3}.\text{14} \right)\]

Answer:

                Side of the square piece = 6 cm \[\therefore \]                  Area of the square piece           \[~={{(\text{side})}^{\text{2}}}={{\left( \text{6} \right)}^{\text{2}}}\text{c}{{\text{m}}^{\text{2}}}\] \[=\text{6}\times \text{6 c}{{\text{m}}^{\text{2}}}=\text{36 c}{{\text{m}}^{\text{2}}}\] Area of the circle of radius 2 cm \[\text{=  }\!\!\pi\!\!\text{  (2}{{\text{)}}^{\text{2}}}\text{ c}{{\text{m}}^{\text{2}}}\] \[\text{= 3}\text{.14  }\!\!\times\!\!\text{  4 c}{{\text{m}}^{\text{2}}}\] \[\text{= 12}\text{.56 c}{{\text{m}}^{\text{2}}}\] \[\therefore \] Area of the left over aluminium sheet \[=\text{36 c}{{\text{m}}^{\text{2}}}-\text{12}.\text{56 c}{{\text{m}}^{\text{2}}}\] \[=(\text{36}-\text{12}.\text{56})\text{ c}{{\text{m}}^{\text{2}}}\] \[=\text{23}.\text{44 c}{{\text{m}}^{\text{2}}}.\]