the dimensions of a cuboid are in a ratio 3:2:1 and the total surface area is 1078cm^2 find the length of its on diagonal
Answers
757cm i think it is correct answer
Given :-
- The dimensions of a cuboid are in the ratio 3:2:1
- Total surface area of the cuboid = 1078cm²
Aim :-
- To find the length of it's diagonal.
Ratio :-
Ratio is the comparison of any two or more quantities represented in it's simplest form.
The dimensions of the cuboid :- 3:2:1 is thus in it's reduced form. Hence, let
The common factor by which these dimensions were cancelled out be x.
Therefore, the dimensions will be :- 3x, 2x and 1x respectively.
Total surface area :-
The total surface area of the cuboid is :-
- l represents length
- b represents breadth
- h represents height
Substituting the values,
Adding the terms,
Transposing 2 to the other side,
Reducing to the lowest terms,
Transposing 11 to the other side,
Reducing to the lowest terms,
Transposing the power,
Now that we have the value of x, the dimensions of the cuboid will be :-
- 21 cm(3×7)
- 14 cm (2×7)
- 7 cm (1×7)
Verification :-
Let us verify the value of x.
Adding,
LHS (Left hand side of the Equation) :-
➜ 1078
RHS (Right Hand Side of the Equation) :-
➜ 2(539)
➜ 1078
LHS and RHS are matching.
Hence verified.
Now that we have verified the values, let's find the length of the diagonal.
Diagonal :-
The diagonal of the cuboid :-
Substituting the values,
Therefore the diagonal of the cuboid is 7√14 cm
Some more formulas :-
- Total surface area of a cube = 6a²
- The length of the diagonal = √3a
- Total surface area of a cylinder = 2πrh + 2πr²