Crazy Cube Geometry !

Level pending

A cube with side $10m$ is drilled through two of its adjacent faces of its lateral sides . It makes a deep hole through the cube in the shape of a square of side $6m$ as shown Let $T$ and $V$ be its total surface area and volume respectively ,

If $\dfrac{T}{V}$ can be written in the form $\dfrac{a}{b}$ , where $a$ and $b$ are coprime,

Find $a + b$ .

The answer is 76.

1 solution

Sebastian Linares
Oct 17, 2015

To find V is pretty easy, just get the volume of the whole cube and subtract the smaller cube and the 4 "lids": $10^{3} - 6^{3} - 4(2 \times 6 \times 6) = 496$ To get T, add up the 2 normal faces, the 4 portrait-ish faces, the 8 internal sides of the columns and the 2 cornerless squares: $2(100) + 4(100-36) + 8(12) + [100 - 4(4)] = 720$

$\frac{720}{496} = \frac{45}{31}$

Finally, $31 + 45 = 76$

Great job! Thanks for the solution. Voted you up!

Priyansh Sangule - 5 years, 7 months ago

Crazy Cube Geometry !

The answer is 76.

1 solution

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