If each edge of a cube is doubled |
(a) How many times will its surface area increase? |
(b) How many times will its volume increase? |
Answer:
(a) Let the edge of cube be x According to question, edge of cube is doubled = 2x The surface area of cube when edge is doubled = \[6{{l}^{2}}\] \[=\text{ }6\times {{\left( 2x \right)}^{2}}\] \[=\text{ }6\text{ }\times 4{{x}^{2}}\] \[=\text{ }4\text{ }x\text{ }\left( 6{{x}^{2}} \right)\] The surface area of cube is 4 time increase. (b) The volume of cube when edge is doubled \[={{(2x)}^{3}}\] \[=8{{x}^{3}}\] The volume of cube is 8 time increase, when edge is doubled.
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