What is the surface area of the cuboid C ?

Question

What is the surface area of the cuboid C ? (1) The length of the diagonal of C is 5 (2) The sum of the sides of C is 10 I came up with this question while writing the 3-d geometry section. I think its a decent question actually :-D

... The link also has a solution to it

prab · Answer

by surface area do you mean the surface area of onlu 4 walls or the total surface area

Raths · Answer

(a + b + c)^2 - (a^2 + b^2 + c^2) = surface area of cuboid...
both are reqd...hence C according to me..

Spidy001 · Answer

surface area of a cuboid = 2(lb+bh+lh)

1. Not sufficient

length of the diagonal in a cuboid = sqrt(l^2+b^2+h^2) = 5

=>l^2+b^2+h^2 = 25

but this is not enough to answer the question as we can go with different l,b,h combination

2. Not sufficient

l+b+h = 10

different l,b and h values will yield different surface area.

l b h
 8 1 1
 7 2 1

together, its sufficient

(l+b+h)^2 = l^2+b^2+h^2+2(lb+bh+lh)

Answer is C.

cano · Answer

The formulas you are using are for cuboids with right angles only, right? Otherwise I think it's E.

Spidy001 · Answer

No. i think answer would still be C.

Even if angle changes l , b and h would still be the same. Total surface area has nothing to do with angles.

It would still be 2(lb+bh+lh). Hope its clear now.

GMATmission · Answer

I did a silly mistake here..may be you also did the same...I read cuboid as cube :ouch

gautammalik · Answer

To find S = 2(ab + bc + ca), where a, b, c are sides of a cuboid

(1) d^2 = a^2 + b^2 + c^2 = 25
Not sufficient

(2) a + b + c = 10
Not sufficient

(3) Comibining (1) and (2)
 a^2 + b^2 + c^2 = 25
(a + b + c)^2 = 100 => a^2 + b^2 + c^2 + 2(ab + bc + ca) = 100
25 + 2(ab + bc + ca) = 100
2(ab + bc + ca) = 75

Hence (C)

krrish · Answer

here it is for u

S!: givens (l^2 + b^2 h^2)^1/2 value, 
s2: gives u l+b+h value now square s2 and subtract from 1 we get 2 (lb +bh+lh) so combines s1 and s2 are sifficient

bumpbot · Answer

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What is the surface area of the cuboid C ?

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