Question

How many cubes of edge 20cm can be placed in a box of measurement 6m×2m×1m.​

Answer 1

Given

Edge of cube is 20cm

Measurement of box 6m×2m×1m

To Find

No of cubes which can be placed in a box of 6m×2m×1m

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Step by step explanation

1. First we will find the volume of box where it's dimensions is given.
2. After finding volume of box we will find volume of cubes.
3. At last we will divide the volume of box by volume of cube.The resultant is our require answer.

Box is generally in the form of a cuboid so ,we'll apply here volume of cuboid because box is in the shape of a cuboid.

Volume of box =length×breadth ×height

Volume of box =6×2×1=12m³

Now, we have to find volume of cube

Volume of cube =(side)³

Volume of cube =20cm

Note : side is given in cm we have to divide it by 100 or multiply with ${10}^{ - 2}$.

Volume of cube =>20×${10}^{ - 2}$.

Number of cube=volume of box ÷volume of each cube

$\sf \: Number \: of \: cubes = \dfrac{12}{20 \times {10}^{ - 2} }$

$\sf \: Number \: of \: cubes = \dfrac{3}{5 \times {10}^{ - 2} }$

$\sf \: Number of cubes = \dfrac{3 \times 100 }{5} = 3 \times 20 = 60$

∴60 cubes can be placed in a box of measurement 6m×2m×1m