A wooden cuboid is 24 cm by 30 cm by 36 cm. Cubes of equal sides are cut off from all its corners. The volume of the remaining block is $20088 c m^{3} .$ What is the length of the edge of each cube cut off from the cuboid?

6 cm

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9 cm

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1 cm

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7 cm

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Solution

The correct option is B 9 cm
Volume cut = Initial volume of cuboid – volume of remaining figure
$= ((24 \times 30 \times 36) - 20088) c m^{3} = (25920 - 20088) c m^{3} = 5832 c m^{3}$
So, Volume of each of the smaller cubes
V = $(\frac{5832}{8}) c m^{3} (one for each corner for a total of 8 corners) = 729 = (9)^{3} c m^{3}$
So, Length of a side of smaller cubes = 9 cm

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A wooden cuboid is 24 cm by 30 cm by 36 cm. Cubes of equal sides are cut off from all its corners. The volume of the remaining block is 20088 cm3. What is the length of the edge of each cube cut off from the cuboid?

A wooden cuboid is 24 cm by 30 cm by 36 cm. Cubes of equal sides are cut off from all its corners. The volume of the remaining block is $20088 c m^{3} .$ What is the length of the edge of each cube cut off from the cuboid?