string in a cube

Geometry Level 1

In a hollow cube of side length 12, we attached a string from the center of the top surface to one of the corners at the bottom surface. What is the length of the string?

aprox. 14.7 aprox.17.3 aprox.3.5 aprox.8.5

Daniel Chadwick by daniel chadwick , 20, Australia

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2 solutions

Krishna Garg
Aug 28, 2014

With given details, we calculate first diagonal distance of base of cube having 12 cm length ,that is 12 underroot 2. Now,considering top point in middle of top of cube and string to one of bottom corner it is a triangle with base 12 underroot 2/2 , height 12 cm and length of string with this will be underroot 144+72 = underroot 216 that is appox 14.7 cm Ans K.K.GARG India

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Applying Pythagoras theorem .(Length of the string)square equals one side means 12 square and half the length of the top face Square diagonal which is 6 multiplied by root 2 Square.

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My solution involves finding the hypotenuse of a rt triangle with sides 18 and 6. My answer is 18.97. The closest choice given was 17.3. Solution Solution

Guiseppi Butel - 6 years, 11 months ago

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(I believe that) The intention of this question is that the cube was hollow, and the string is the straight line distance, which would give us 6 2 + 6 2 + 1 2 2 \sqrt{ 6^2 + 6^2 + 12^2 } .

I've updated the phrasing of the question accordingly.

Calvin Lin Staff - 6 years, 10 months ago

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Thanks, Calvin.

Guiseppi Butel - 6 years, 10 months ago

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