question_answer 1)

                If each edge of a cube is doubled, (i) how many times will its surface area increase? (ii) how many times will its volume increase?

Answer:

                Let the original edge of the cube be a cm. Then, its new edge \[=2a\,\,cm\] (i) Original surface area of the cube \[=6{{a}^{2}}\,c{{m}^{2}}\] New surface area of the cube                 \[=6{{(2a)}^{2}}\,c{{m}^{2}}\] \[=24{{a}^{2}}\,c{{m}^{2}}\] \[=4\,(6{{a}^{2}}\,c{{m}^{2}})\] = 4 original surface area, Hence, its surface area will increase 4 times. (ii) Original volume of the cube \[={{a}^{3}}\,c{{m}^{3}}\] New volume of the cube \[={{(2a)}^{3}}\,c{{m}^{3}}\]                 \[=8{{a}^{3}}\,c{{m}^{3}}\] = 8 original volume of the cube. Hence, its volume will increase 8 times.