The volume of a cuboid is 5a² - 80b². Which of the options below can be possible dimensions of the cuboid?

Correct option is B

Given :

The volume of the cuboid(V) = 5a$$^2$$-80b$$^2$$ 

Formula Used: 

​The volume of the cuboid;

V = Length × Breadth × Height  

Solution: 

Analyzing the each option :

Option (a): 5 , 2a−b , 2a+b

The volume would be:

V=5 × ( 2a − b ) × ( 2a + b )

V = 5 × ( 4a$$^2$$ − b$$^2$$ ) = 20a$$^2$$ − 5b$$^2$$​

So, option (a) is not correct.

Option (b): 5 , a−4b , a + 4b

The volume would be:

V = 5 × ( a − 4b ) × ( a + 4b )

V = 5 × ( a$$^2$$ − 16b$$^2$$ ) = 5a$$^2$$ − 80b$$^2$$​

This is equal to $$5a^2 - 80b^2$$​

So, option (b) is correct

Option (c): 5 , a−b , a+4b

V=5 × ( a − b ) × ( a + 4b )

​$$V = 5 \times (a^2 + 3ab - 4b^2)$$​​

So option (c) is not correct.

Option (d): 5 , 2a−b , a+2b

The volume would be:

V = 5 × ( 2a − b ) × ( a + 2b )

V = 5 × ( 2a$$^2$$ + 3ab − 2b$$^2$$ ) =10a$$^2$$​+15ab − 10b$$^2$$​

So option (d) is not correct.

The, possible dimensions of the cuboid : 5 , a−4b , a + 4b

Hence, Option (b) is correct answer