question_answer 1)

                Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?                 (a)                                          (b)

Answer:

                Volume of cylinder B is greater. For Cylinder A \[r=\frac{7}{2}\,cm\] \[h=14\,cm\]  \[\therefore \] Volume \[=\pi {{r}^{2}}h\] \[=\frac{22}{7}\times \frac{7}{2}\,\times \frac{7}{2}\,\times 14\] \[=539\,c{{m}^{3}}\] For Cylinder B \[r=\frac{14}{2}\,cm\,=7\,cm\] \[h=\,7\,\,cm\] \[\therefore \]  Volume \[=\pi {{r}^{2}}h\] \[=\frac{22}{7}\,\times 7\times 7\times 7\] \[=1078\,c{{m}^{3}}\]. By actual calculation of volumes of both, it is verified that the volume of cylinder B is greater. For Cylinder A Surface area \[=2\pi r\,(r+h)\] \[=2\times \frac{22}{7}\,\times \frac{7}{2}\ \times \,\left( \frac{7}{2}\,+14 \right)\] \[=2\times \,\frac{22}{7}\,\times \frac{7}{2}\,\times \frac{35}{2}\] \[=385\,c{{m}^{2}}\] For Cylinder B Surface area \[=2\pi r(r+h)\]                 \[=2\times \frac{22}{7}\,\times \frac{7}{2}\,\times \left( \frac{7}{2}+14 \right)\] \[=2\times \frac{22}{7}\times \,\frac{7}{2}\,\times \frac{35}{2}\] \[=385\,c{{m}^{2}}\] For Cylinder B Surface area \[=2\pi r\,(r+h)\] \[=2\times \frac{22}{7}\times 7\times (7+7)\] \[=2\times \frac{22}{7}\times 7\times 14\] \[=\,616\,c{{m}^{2}}\]. By actual calculation of surface area of both, we observe that the cylinder with greater volume has greater surface area.