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SURFACE AREA

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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Mar 18, 2012 4:51 am
pappueshwar wrote:What is the surface area of cuboid C?

1. The length of the diagonal of C is 5.
2. The sum of the sides of C is 10.

OA IS C
If l = length, b = width and h = height of cuboid (rectangular prism), then
Surface area of a cuboid = 2(lb + bh + lh)

(1) The length of the diagonal of C is 5.
Length of the diagonal in a cuboid = √(l² + b² + h²)
So, √(l² + b² + h²) = 5 or (l² + b² + h²) = 25, which is definitely NOT sufficient to find the surface area of C.

(2) The sum of the sides of C is 10 implies l + b + h = 10, which is again NOT sufficient to find the surface area of C.

Combining (1) and (2):
(l + b + h)² = (l² + b² + h²) + 2(lb + bh + lh)
(10)² = 25 + 2(lb + bh + lh), solving which we can find the surface area of C; SUFFICIENT.

The correct answer is C.
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by pappueshwar » Sun Mar 18, 2012 5:28 am
Anurag,

how did u get this ?

(l + b + h)² = (l² + b² + h²) + 2(lb + bh + lh)
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by Anurag@Gurome » Sun Mar 18, 2012 8:04 pm
pappueshwar wrote:Anurag,

how did u get this ?

(l + b + h)² = (l² + b² + h²) + 2(lb + bh + lh)
I hope you know the identity using 2 variables:
(a + b)² = (a + b)(a + b) = a² + b² + 2ab (you can also do this using FOIL method)

In the same way, for 3 variables,
(a + b + c)² = (a + b + c)(a + b + c) = (a² + b² + c²) + 2(ab + bc + ac)
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by ubhanja » Mon Mar 19, 2012 8:53 am
Had this been a cube instead of cuboid, answer D would have been correct I believe.
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by Anurag@Gurome » Mon Mar 19, 2012 8:48 pm
ubhanja wrote:Had this been a cube instead of cuboid, answer D would have been correct I believe.
Surface area of a cube = 6a², where a is each of the sides of a cube.

(1) The length of the diagonal of cube is 5.
Length of the diagonal in a cube = a√3
So, a√3 = 5
We can find a from the above equation and hence we can find the surface area of cube; SUFFICIENT.

(2) The sum of the sides of C is 10.
3a = 10 implies a = 10/3
So, we can find the surface area of cube; SUFFICIENT.

The correct answer is D in case of a cube.
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