Question

the dimensions of a rectangular box are in a ratio 2:3:4 and the difference between the cost of covering it with sheet of paper at the rate of rs.4 and rs4.50 per m² is rs.416 . find the dimension of the box

Answer 1

Answer:

${\huge{\underline{\underline{\sf{\blue{Solution :-}}}}}}$

Let the dimensions of the rectangular box be 2x , 3x and 4x in metres.

Surface area of the box

= 2 ( lb + bh + hl ) sq. units

= 2 ( 2x × 3x + 3x × 4x + 4x × 2x ) m ^{2}

= 2 ( 6x^{2} + 12x^{2} + 8x^{2} ) m^{2} = 52x ^{2} m ^{2}

Cost of covering the box at the rate of ₹ 4 per m ^{2} = ₹ (4 × 52x^{2} ) = 208x^{2}

Cost of covering the box at the rate of ₹ 4.50 per m ^{2} = (4.50 × 52x^{2} ) = 234x^{2}

${\huge{\underline{\underline{\sf{\blue{Given :-}}}}}}$

Difference in both the cost = ₹ 416

Therefore ,

224x^{2} - 208x^{2} = 416

= > 26x ^{2} = 416

$= > x ^{2} = \frac{416}{26} = 16 = > x = 4$

Thus,

The demensions of the box are

2x = 2 × 4 m = 8 m ;

3x = 3 × 4 m = 12 m ;

4x = 4 × 4 m = 16 m

Now ,

Volume of the box = l × b × h

= 8 m × 12 m × 16 m

= 1536 m ^{2}