the ratio of dimensions of cuboidal box is 2 : 3 : 4 the different between cost of wrapping the box at the rate of rupees 4\m square and rupees 4.50 per metres square is rupees 416. find the dimension of the cuboidal box
Answers
TSA = 2(lb+bh+hl)
TSa = 26x
Now., 4.5(26x) - 4(26x) = Rs416 117x-104x = 416 13x=416 x=13
Now you can solve it easily hope this helps.
Answer:
Dimensions of box are 8 m × 12 m × 16 m
Step-by-step explanation:
Given data:
The ratio of the dimensions of cubical box = 2 : 3 : 4
the difference between cost of wrapping the box at rate of 4 Rs/m² and 4.50 Rs/m² = 416 Rs
here we need to find dimensions of cuboidal box
Let 2x m, 3x m, and 4x m are be the dimensions of cuboidal box
[∵ the dimensions are in 2 : 3 : 4 ratio ]
total surface area of the cubical box = 2 (lb+bh+lh)
= 2 [2x(3x) +3x(4x)+4x(2x) ]
= 2[ 6x²+ 12x² + 8x² ]
= 2 [ 26x² ] = 52x² m²
the cost of the wrapping the box at rate 4 Rs/m² = 4(52x²) = 208x²
the cost of the wrapping the box at 4.50 Rs/m² = 4.5(42x²) = 234x²
From given data the difference between cost of wrapping the box at rate of 4 Rs/m² and 4.50 Rs/m² = 416 Rs
⇒ 234x² - 208x² = 416
26x² = 416
x² = 416/26 = 16
x² = 16
x = 4
dimensions of box are
2x = 2(4) = 8 m
3x = 3(4) = 12 m
4x = 4(4) = 16 m