question_answer

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.