Problem Solving

formula for surface area= 2(lb+bh+hl) for any cuboid.
Hence for a cube l=b=h=a thus sa=6a^2
for a cuboid with l=2a, b=a, h=a sa=10a^2

hence ratio is 3/5 it comes out as smple visualization too

Can anyone provide a simpler explanation please?

Rastis wrote:Can anyone provide a simpler explanation please?

Let me take a shot at trying to explain the solution in a simpler way.

1. The cube1 has 6 faces. 2 faces have area as l*b, 2 faces have area as l*h and 2 faces have area as b*h.

Surface area of the Cube1 is sum of all these areas i.e. 2(l*b)+2(l*h)+2(b*h)

Simplifying 2(l*b)+2(l*h)+2(b*h) = 2[(l*b)+(l*h)2(b*h)] ------>(I)

Let us say the l=b=h=1 for this cube.

Hence Surface area of cube1 is now = 2*3 =6

For Cube2, it is given that l=2l i.e. l=2*1=2 and b and h are same as Cube1.

Substitute l=2, b=1 and h=1 in (I) to get the surface area of Cube2. It comes as 2*5=10.

Hence ratio of Surface area of Cube1:Cube2 = 6/10 = 3/5.

OA should be D.

(D) 3/5

Surface area of cube having unit length = 6
The rectangular solid with length as 2 units is same as two cubes each with unit length arranged length wise, thus one surface area (out of 6)of such cube used up leaving the surface area of such rectangular solid = 5 * 2=10

Ratio of surface area of cube and the rectangular solid equals 6:10 or 3:5
=> correct answer is option (D).

Ans: D
Going by pure formulae
Surface area of a Cube: 6S^2 Where S is the length of a side.
Surface area of any rectangular solid is: 2(LB+LH+BH)where the L,B,H correspond to the length, breadth and height(or depth).
Here, it is given that length of the rectagular solid is twice the length of the side of the cube, so consider L=2l then, 2(LB+LH+BH)= 2(2l*l + 2l*l + l*l)= 10(l^2)
whereas the surface area of cube= 6(l^2)
so the Ratio= 6(l^2)/10(l^2)= 6/10= 3/5.

Wow, lots of complicated methods.

A cube has 6 equal faces.

2 cubes joined together will have 12 of these faces - the 2 glued together = 10 total.

6/10 = 3/5

That's it.

IMO: D

In this prob there is no need to think about the dimensions of the cube or the rect. solid. Just assume the area of one face of the cube to be A.
There are 6 such faces in the cube: surface area = 6A.
There are 10 such areas in the rect. solid (join two of the cubes and minus two joining surfaces to get the final surface area): Surface area = 10A.
Ratio = 6/10 = 3/5. D

~Binit.

how this 5 year old question popped up