# Answer to Question #23220 in Geometry for Daryl Ligutan

Question #23220

3.If an edge of a cube is increased by 33%, by how much is the total surface area increased?

Expert's answer

Surface area of a cube S:

S = 6 a^2

a is the length of the side of each edge of the cube

If an edge of a cube is increased by 33%

a' = a + 0.33a = 1.33a

a' =& the new edge of a cube

S' = 6 a'^2 = 6 a^2 *1.33^2 = 1.33^2 *S =& 1.7689*S

S' - Surface area of a new cube

the total surface area increased in

(S'-S)/S *100% = (1.7689 - 1)*100% = 76.89%

Answer:& 76.89%

S = 6 a^2

a is the length of the side of each edge of the cube

If an edge of a cube is increased by 33%

a' = a + 0.33a = 1.33a

a' =& the new edge of a cube

S' = 6 a'^2 = 6 a^2 *1.33^2 = 1.33^2 *S =& 1.7689*S

S' - Surface area of a new cube

the total surface area increased in

(S'-S)/S *100% = (1.7689 - 1)*100% = 76.89%

Answer:& 76.89%

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