The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its surface area is 3150 cm2, find its all the dimensions and also, find its volume.
Answers
Answered by
3
Given :-
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its surface area is 3150 cm²
To Find :-
Dimension and Volume
Solution :-
We know that
Surface Area = 2(lb + bh + lh)
Let the dimension be 6x,5x and 3x
3150 = 2[(6x × 5x) + (5x × 3x) + (6x × 3x)
3150/2 = [(6x × 5x) + (5x × 3x) + (6x × 3x)
1575 = 30x² + 15x² + 18x²
1575 = 63x²
1575/63 = x²
25 = x²
√25 = x
5 = x
Length = 6x = 36 cm
Breadth = 5x = 30 cm
Height = 3x = 15 cm
Now
Volume = lbh
Volume = (36)(30)(15)
Volume = 16200 cm³
Answered by
1
GiVEN
- Ratio of Length : Breadth : Height = 6 : 5 : 3
- Surface Area of Rectangle = 3150 cm²
TO FiND
- All Dimensions & Volume of Rectangle
FORMULA USED
- Surface Area of Rectangle = 2(lb + bh + lh)
- Volume of Rectangle = l × b × h
SOLUTiON
Lets assume the Length, Breadth & Height are 6x, 5x & 3x.
- Surface Area = 2(lb + bh + lh)
- 3150 = 2(6x*5x + 5x*3x + 6x*3x)
- 1575 = 30x² + 15x² + 18x²
- 1575 = 63x²
- x² = 25
- x = 5
- Length = 6*5 = 30 cm
- Breadth = 5*5 = 25 cm
- Height = 3*5 = 15 cm
- Volume of Rectangle = l × b × h
- Volume = 30 * 25 * 15
- Volume = 11250 cm³
▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬
Similar questions