The dimensions of a rectangular 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 Rs. 8 and Rs. 9.50 per square metre is Rs. 1248. Find the dimensions of the box in metres.
A. 2 m, 12 m, 8 m
B. 4 m, 9 m, 16 m
C. 8 m, 12 m, 16 m
D. None of these
Answer: Option C
Solution(By Examveda Team)
Let the length, breadth and height of the box be 2x, 3x and 4x respectivelyThen, surface area of the box :
= 2 [2x.3x + 3x.4x + 2x.4x]
= [2(6x2 + 12x2 + 8x2)]
= 52x2
$$\eqalign{ & \therefore 52{x^2} = \frac{{1248}}{{1.50}} \cr & \Rightarrow 52{x^2} = 832 \cr & \Rightarrow {x^2} = \frac{{832}}{{52}} \cr & \Rightarrow {x^2} = 16 \cr & \Rightarrow x = 4 \cr} $$
Hence, the diameter of the box are 8 m, 12 m and 16 m
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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