question_answer 22)

                Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?

Answer:

                Similarity \[\to \] Both have the same heights. Difference \[\to \] One is cylinder, the other is a cube; Cylinder is a solid obtained by revolving a rectangular area about its one side whereas a cube is a solid enclosed by six faces; a cylinder has two circular faces whereas a cube has six square faces. For First Figure \[r=\frac{7}{2}\,cm\] \[h=7\,cm\] \[\therefore \] Lateral surface area \[=2\pi rh\] \[=2\times \frac{22}{7}\,\times \frac{7}{2}\,\times 7\] \[=154\,\,c{{m}^{2}}\] For Second Figure                 \[l=7\,cm\] \[b=7\,cm\] \[h=7\,cm\] \[\therefore \] Lateral surface area \[=4{{l}^{2}}\] \[=4\times {{(7)}^{2}}\] \[=196\,c{{m}^{2}}\] Hence, the second box has the larger lateral surface area.