a cube and cuboid have same volume. dimentions of cuboid are in the ratio 1:2:4. if the difference betwween the cost of polishingthe cube and the cuboid is at the rate of rs5 /m2 is rs 80, find the volumes
Given that: The dimension of the cuboid are in the ratio 1:2:4. Let length, breadth and height of the cuboid be l, b and h respectively. So,
l = x, b = 2x and h = 4 x
So, Volume of the cuboid = l×b×h = 6x3
Let edge of the cube = a
Thus, volume of the cube = a3
Since, volume of cube and cuboid is same. Therefore,
Surface area of the cube = 6a2 = 6(2x)2 = 24x2
So, cost of polishing the cube @ 5/m2 = Rs (24x2×5) = Rs 120x2
And, surface area of the cuboid
So, cost of polishing the cuboid @ 5/m2 = Rs (28x2×5) = Rs 140x2
Given, the difference between the cost of polishing the cube and cuboid = Rs 80
So,
Thus, Edge of the cube = a = 2x = 2(2) = 4 m
Volume of the cube = a3 = (4)3 = 64 m3
Thus, volume of the cuboid = volume of the cube = 64 m3