Question

A cuboid measures 24m×12m×10m. How many cubes of side 3m can fit in the box? ( 9 / 16 / 15 / 24) ​

Answer 1

Correct answer is 96 cubes.

• If we want to fit a cube of size 3 × 3 × 3 then we should have the cuboid of the lengths of the multiples of the cube .
• As we can see that the cuboid consists of sides 24,12 and 10.
• 24 and 12 are multiples of 3 but 10 is not a multiple of 3 .
• So we consider a length that is multiple of 3 to obtain exact number of cubes fitted inside the cuboid.
• To consider the length we know 3 , 6 and 9 are multiples of 3 (we need to consider least multiple of 3 less than the number(< 10))
• Now calculating the volume of the cuboid
• Volume = 24 × 12 × 9 = 2592 sq m
• Now calculating the volume of the cube = 3 × 3 × 3 = 27 sq m
• Now to obtain the number of cubes that could fit in the cuboid we divide the volume of cuboid with the volume of cube.

No. of cubes = $\frac{Volume of cuboid}{Volume of cube}$

No. of cubes = $\frac{2592}{27}$

No. of cubes = 96