question_answer 1)

                Find the height of the cylinder whose volume is \[1.54\,\,{{m}^{3}}\] and diameter of the base is 140 cm?     

Answer:

                \[\because \] Diameter of the base = 140 cm \[\therefore \] Radius of the base (r) \[=\frac{140}{2}\,cm\,=70\,cm\] \[\therefore \] Area of the base \[=\pi {{r}^{2}}\] \[=\frac{22}{7}\times 70\times 70\] \[=15400\,c{{m}^{2}}\] Volume of the cylinder \[=1.54\,\,{{m}^{3}}\] \[=1.54\,\times 100\times 100\,\times 100\,c{{m}^{3}}\] \[=1540000\,c{{m}^{3}}\] \[\therefore \] Height of the cylinder   \[=\frac{\text{Volume}\,\text{of}\,\text{the}\,\text{cylinder}}{\text{Area}\,\text{of}\,\text{the}\,\text{base}\,\text{of}\,\text{the}\,\text{cylinder}}\] \[=\frac{1540000}{15400}\] \[=100\,cm\] \[=\,1\,m\] Hence, the height of the cylinder is \[\,1\,m\].