If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu.cm; then the length of the shortest side is :
A. 10 cm
B. 15 cm
C. 20 cm
D. 30 cm
Answer: Option B
Solution(By Examveda Team)
Let lb = 2x, bh = 3x and lh = 4xThen,
$$\eqalign{ & 24{x^3} = {\left( {lbh} \right)^2} = 9000 \times 9000 \cr & \Rightarrow {x^3} = 375 \times 9000 \cr & \Rightarrow x = 150 \cr} $$
So, lb = 300, bh = 450, lh = 600 and lbh = 9000
$$\eqalign{ & \therefore h = \frac{{9000}}{{300}} = 30 \cr & l = \frac{{9000}}{{450}} = 20\& \cr & b = \frac{{9000}}{{600}} = 15 \cr} $$
Hence, shortest side = 15 cm
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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