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.
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