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
Surface Area of Rectangular Solid
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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.
-BM-
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.
-BM-
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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
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