(N.C.E.R.T.)
The dimensions of the cuboidal box are in the ratio 2 : 3:4 and the difference between the cost
of covering it with sheet of paper at the rate of 4 and ²4-50 per m’ is 416. Find the
dimensions of the box.
Answers
Answer:
Que. rectangular box 2:3:4
length=2x
breadth =3x
height =4x
surface Area =2(2x.3x+3x.4x+4x.2x)
=2(6x2+12x2+8x2)
=52x2
→9.5×52x2−8×52x2=1248
∴1.5×52x2=1248
∴x2=1.5×521248 ∴x2=16x=4
→l=2x=8cm,b=3x=12cm,h=4x=16cm.
Answer:
Step-by-step explanation:
Dimensions of rectangular box are in the ratio 2:3:4.
Let the -
length of rectangular box = 2x
breadth of rectangular box = 3x
height of rectangular box = 4x
Curved surface area of cuboid = 2(lb + bh + hl)
Substitute the known values in above formula
=> 2[(2x × 3x) + (3x × 4x) + (4x × 2x)]
=> 8 (6x² + 12x² + 8x²)
=> 8(26x²)
=> 52x² m²
Now,
Cost of painting at Rs. 4 = 52x² × 4
=> Rs. 208x²
Cost of painting at Rs. 4.50 = 52x² × 4.50
=> Rs. 234x²
Difference between costs = Rs. 416
=> Rs. 234x² - Rs. 208x² = Rs. 416
=> Rs. 26x² = Rs. 416
=> 26x² = 416
=> x² = 16
=> x = 4
So,
Length of cardboard = 2x
=> 2(4)
=> 8 m
Breadth of cardboard = 3x
=> 3(4)
=> 12 m
Height of cardboard = 4x
=> 4(4)
=> 16 m
•°• Dimensions are 8m, 12m and 16m