Cutting a cuboid

Geometry Level pending

A $3\times 5\times 6$ cuboid was cut into smaller cubes of dimension $1\times 1\times 1$ . What is the ratio of the surface area of the $3\times 5\times 6$ cuboid to the total surface area of the $1\times 1\times 1$ cubes. If your answer can be expressed as $\dfrac{a}{b}$ , where $a$ and $b$ are positive coprime integers, submit your answer as $a+b$

The answer is 37.

1 solution

A Former Brilliant Member
Apr 12, 2018

Relevant wiki: Surface Area of a Cuboid

The surface area of the original cuboid is $2(3(5)+3(6)+5(6)] = 126$

Since the original cuboid is divided into unit cubes, the number of unit cubes is also the volume of the original cuboid. So the number of unit cubes is

$3(5)(6)=90$

and the total surface area of the unit cubes is

$90(6)(1^2) = 540$

The desired ratio is $\dfrac{126}{540} = \dfrac{7}{30}$

and the desired answer is $7+30=\boxed{37}$

Cutting a cuboid

The answer is 37.

1 solution

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