Question

A CUBE AND A CUBOID HAVE THE SAME VOLUME.THE DIMENSIONS OF THE CUBOID ARE IN THE RATIO 1:2:4.IF THE DIFFERENCE BETWEEN THE COST OF POLISHING THE CUBOID AND THE CUBE AT THE RATE OF RS.5 PER SQUARE METER IS RS.8O.FIND THEIR VOLUMES.

Answer 1

Let the sides of the cube be a. Then the volume of the cube is a3.

 

Let the smallest side of the cuboid be x. Then, the other two sides are 2x and 4x, since the sides are in the ratio of 1:2:4.

 

Then, the volume of the cuboid is x*2x*4x = 8x3

 

Then, a3 = 8x3, or a = 2x.

 

The total surface area of the cube = 6a2

 

The total surface area of the cuboid = 2*(x*2x+2x*4x+x*4x) = 2*(2x2+8x2+4x2) = 28x2

 

The cost of polishing the cube = 5*6a2 = 30a2

 

Cost of polishing the cuboid = 5*28x2 = 140x2

 

The difference between the cost of polishing the cuboid and cube is Rs. 80

 

i.e. 140x2 - 30a2 = 80

 

But a = 2x. Substituting the value of a in the above equation, we get

 

140x2 – 30*4x2 = 80

 

140x2 – 120x2 = 80

 

Or 20x2 = 80

 

Or x2 = 80/20 = 4

 

Thus, x = sqrt(4) = 2.

 

If x = 2, then a = 2x = 2*2 = 4

 

And the other sides of the cuboid are 2x and 4x, which gives 2*2 and 4*2, or 4 and 8.

 

Thus, the volume of the cube and cuboid are 4*4*4 or 2*4*8, which gives 64.

Answer 2

Let the sides of the cube be a. Then the volume of the cube is a3.

 

Let the smallest side of the cuboid be x. Then, the other two sides are 2x and 4x, since the sides are in the ratio of 1:2:4.

 

Then, the volume of the cuboid is x*2x*4x = 8x3

 

Then, a3 = 8x3, or a = 2x.

 

The total surface area of the cube = 6a2

 

The total surface area of the cuboid = 2*(x*2x+2x*4x+x*4x) = 2*(2x2+8x2+4x2) = 28x2

 

The cost of polishing the cube = 5*6a2 = 30a2

 

Cost of polishing the cuboid = 5*28x2 = 140x2

 

The difference between the cost of polishing the cuboid and cube is Rs. 80

 

i.e. 140x2 - 30a2 = 80

 

But a = 2x. Substituting the value of a in the above equation, we get

 

140x2 – 30*4x2 = 80

 

140x2 – 120x2 = 80

 

Or 20x2 = 80

 

Or x2 = 80/20 = 4

 

Thus, x = sqrt(4) = 2.

 

If x = 2, then a = 2x = 2*2 = 4

 

And the other sides of the cuboid are 2x and 4x, which gives 2*2 and 4*2, or 4 and 8.

 

Thus, the volume of the cube and cuboid are 4*4*4 or 2*4*8, which gives 64.Answer:

Step-by-step explanation:

Hope this helps