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Surface Area of Rectangular Solid

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by cubicle_bound_misfit » Tue Mar 31, 2009 3:01 am
I have certain doubts about this one. Gurus can you please help?

In the rectangular solid, if AB=5, what is the surface area of the solid?

1. BC=8
2. The volume of the solid = 80
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by bluementor » Tue Mar 31, 2009 3:56 am
Notation:
AB = a = 5
BC = b
CD = c

Surface area, S = 2ab + 2ac + 2bc
Volume, V = abc

Statement 1: b=8

We still don't know anything about c, hence insufficient.

Statement 2: V=80

abc = 80
5bc = 80
bc = 16

S = 2a(b + c) +2(16)

We still don’t know c, hence insufficient.

Both statements together:

Substitute b=8 into bc=16 to evaluate c. We can now work out the surface area, S. Sufficient. Choose C.

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by iwant700plus » Tue Mar 31, 2009 4:01 am
Surface area = 2lw+2lh+2hw = 2(lw+lh+hw)=2(5(w+h)+wh)

Let l=AB=5. What is w and h?

1) Let w=BC=8. Insufficient, no info about h.
2)V=lwh=80-->5wh->wh=16. While this gives us wh, it gives different values for w+h e.g 4*4=16, w+h=8 but for 2*8=16, 2+8=10. Insufficient.

Taken together
From stmt 1, we know w=8
So wh=16-->8h=16, h=2.

With all the dimensions, we can calculate surface area. Sufficient.

IMO, Ans is C
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