Difference between revisions of "2008 iTest Problems/Problem 38"
Rockmanex3 (talk | contribs) (Solution to Problem 38) |
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==Problem== | ==Problem== | ||
− | The volume of a certain rectangular | + | The volume of a certain rectangular solid is <math>216\text{ cm}^3</math>, its total surface area is <math>288\text{ cm}^2</math>, and its three dimensions are in |
− | geometric progression. Find the sum of the lengths in cm of all the edges of this solid. | + | geometric progression. Find the sum of the lengths in cm of all the edges of this solid. |
==Solution== | ==Solution== |
Latest revision as of 17:08, 15 March 2021
Problem
The volume of a certain rectangular solid is , its total surface area is
, and its three dimensions are in
geometric progression. Find the sum of the lengths in cm of all the edges of this solid.
Solution
Let the three side lengths be ,
, and
. Because the volume of the solid is
,
The surface area of the solid is
, so
Note that the sum of the side lengths of the cube is
and that the equation above has a similar form.
The sum of all the edges of the cube is
centimeters.
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 37 |
Followed by: Problem 39 | |
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