How much percent is the decreased?

Geometry Level 2

If the surface area of a cube is decreased by 20%, how much percent is the decreased in each edge? Round your answer to 2 decimal places.


The answer is 10.56.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

let 1 unit be the edge length of the original cube, the surface area is

S = S= ( 6 ) ( 1 2 ) = 6 (6)(1^2) = 6 square units

now the decreased surfaced area is

s = 0.8 ( 6 ) = 4.8 s = 0.8(6) = 4.8 square units

the decreased edge length is

4.8 = 6 ( x 2 ) 4.8 = 6(x^2)

x = 0.894427191 x = 0.894427191 units

the percent decreased in edge is

% decreased = 1 − 0.894427191 1 ( 100 ) = 10.56 \frac{1 - 0.894427191}{1} (100) = 10.56 %

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