If the volume of a cuboidal tank is 2x²y². The possible dimensions i.e. length, breadth and height are respectively:
A) 2x, xy, y²
B) 2,x²,y², z
C)2x,xy,y
D) 2, x, x, y, y
Answers
Answer:
D) 2, x, x, y, y
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Given :- The volume of a cuboidal tank is 2x²y².
To Find :- The possible dimensions i.e. length, breadth and height are respectively :-
A) 2x, xy, y²
B) 2,x²,y², z
C)2x,xy,y
D) 2, x, x, y, y
Formula used :-
- Volume of cuboid = Length × Breadth × Height .
Solution :-
we have,
→ Volume of cuboidal tank = 2x²y² .
checking all given options in above told formula we get,
A) 2x, xy, y²
→ Volume = Length × Breadth × Height
→ 2x²y² = 2x × xy × y²
→ 2x²y² = 2 × x × x × y × y²
using a^m × a^n = a^(m + n)
→ 2x²y² = 2 × x^(1 + 1) × y^(1 + 2)
→ 2x²y² = 2 × x² × y³
→ 2x²y² ≠ 2x²y³
therefore, Option (A) is not possible .
B) 2,x²,y², z
→ Volume = 2 × x² × y² × z
→ 2x²y² ≠ 2x²y²z
therefore, Option (B) is not possible .
C) 2x,xy,y
→ Volume = 2x × xy × y
→ 2x²y² = 2 × x × x × y × y
using a^m × a^n = a^(m + n)
→ 2x²y² = 2 × x^(1 + 1) × y^(1 + 1)
→ 2x²y² = 2x²y²
Since LHS is equal to RHS . Therefore, Option (C) is possible .
D) 2, x, x, y, y
→ Volume = 2 × x × x × y × y
→ 2x²y² = 2 × x × x × y × y
using a^m × a^n = a^(m + n)
→ 2x²y² = 2 × x^(1 + 1) × y^(1 + 1)
→ 2x²y² = 2x²y²
here, LHS is equal to RHS but 5 dimensions of cuboidal tank are given . Therefore, Option (D) is not possible .
Hence, we can conclude that, The possible dimensions i.e. length, breadth and height of given cuboidal tank are Option (C) 2x, xy and y .
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