# The volume of a cubical box is 32.768m3. Find the length of each edge

1
by rajaumer

2015-07-23T17:33:18+05:30
Let the length of cubical box = a meter
given volume of box = 32.768 m³

⇒ a³ = 32.768 m³
⇒ a = ∛32.768
⇒ a = 3.2 m

Length of each edge is 3.2m

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To find cube root of 32.768:

1. Write it without the decimal, so it becomes 32768
2. Identify the last three digits and make groups of three three digits from right side. That is 32768 can be written as    "32,   768"
3. Take the last group which is 768.  The last digit of 768 is 8. If the last digit of the perfect cube = 8, the last digit of the cube root = 2. So unit digit of cube root is 2.
4.
Take the next group which is 32 .Find out which maximum cube we can subtract from 32 such that the result >= 0.
We can subtract 3³ = 27 from 32 because 32 - 27 = 5 (If we subtract 4³ = 64 from 4,   32 – 64 = -32 which is < 0)
Hence the tens digit comes as 3.

So we get 32 as answer.
We see that there are 3 digits after the decimal in 32.768. So in its cuberoot, only one digit will be there after the decimal. So answer is 3.2.