The length, breadth and height of a cubical box are in the ratio 5:3:2 and its total surface area is 1550 CM square. find the dimensions of the cubical box.
Answers
Answer:
given length,breadth, height=5:3:2
Step-by-step explanation:
total surface area= 2(lb+bh+lh).
=2(5×3+3×2+5×2)
=2(15+6+10)
=2(31)
=62 cm
Calculation of Dimensions of Cubical Box
Answer: dimension of cubical box is length = 25 cm , breadth = 15cm and height = 10 cm that is 25 cm x 15 cm x 10 cm
Explanation:
Given that length , breadth and height of a cubical box are in ratio 5:3:2
Total Surface area of box = 1150 cm²
Need to find the dimensions of the cubical box
As ratio of length , breadth and height is 5 : 3 : 2
lets assume length = 5y cm , breadth = 3y cm and height = 2y cm
Formula of total surface area of cuboid = 2( l x b + b x h + l x h ) where l is length , b is breadth and h is height
On substituting given value of total surface area and assumed values of length , breadth and height in above formula we get
1550 = 2 ( 5y x 3y + 3y x 2y + 5y x 2y )
=> 1550 = 2 ( 15y² + 6y² + 10y²)
=> 1550/2 = 31y²
=> 775/31 = y²
=> 25 = y²
=> y = √25 = 5
length = 5y = 5 x 5 = 25cm
breadth = 3y = 3 x 5 = 15cm
height = 2y = 2 x 5 = 10cm
Hence dimension of cubical box is length = 25 cm , breadth = 15cm and height = 10 cm that is 25 cm x 15 cm x 10 cm
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