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Each dimension of a rectangular solid is an integer less than 11. The

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Bunuel
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Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 01:15
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Each dimension of a rectangular solid is an integer less than 11. The volume of the solid is 30. If the height of the solid is 10, what is the surface area of the solid?

A. 30
B. 33
C. 66
D. 86
E. 116


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Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 01:29
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Volume = lbh
30 =lbh
lb*10 = 30
lb = 3
Let, l = 3 and b = 1

Surface area = 2(lb+bh+hl)
S.A. = 2(3+10+30)
S.A = 2(43)
S.A.= 86 (which is same for b= 3 and l = 1)

Answer is D
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Re: Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 02:11
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CONCEPT: Volume of solids(rectangular)=Length(l)*Breadth(b)*height(h)
T.S.A of solids = 2(lb+ bh+ lh)

Given-
l*b*h = 30
=> l *b*10 = 30 =>lb=3=3 x 1 [As, Height=10 units]
Thus, length =3 ; breadth=1;height=10
(Since 3 is a prime number and cannot be further factorized)

Total Surface Area(T.S.A) = 2(lb+ bh+ lh)
= 2(3+10+30)=86 square units (D)

Hope this helps. Keep studying. :)
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Re: Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 05:04
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Bunuel wrote:
Each dimension of a rectangular solid is an integer less than 11. The volume of the solid is 30. If the height of the solid is 10, what is the surface area of the solid?

A. 30
B. 33
C. 66
D. 86
E. 116


abc=10bc=30
bc=3=3*1 (integers<11)
sarea: 2(ab+ac+bc)
2(10+3+30)=2(43)=86
(D)
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Re: Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 05:07
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ANSWER IMO D
Volume = 30 = 10 x lb => lb=3
b or l must be 3 or 1.

So, Surface Area = 2 x (3x1 + 3x10 + 10x1) = 86

Bunuel wrote:
Each dimension of a rectangular solid is an integer less than 11. The volume of the solid is 30. If the height of the solid is 10, what is the surface area of the solid?

A. 30
B. 33
C. 66
D. 86
E. 116


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Re: Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 13:05
The important key to answer this questions is to keep in mind that sides are integer only.
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Re: Each dimension of a rectangular solid is an integer less than 11. The [#permalink] New post   24 Nov 2020, 20:53
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Each dimension of a rectangular solid is an integer less than 11. The volume of the solid is 30. If the height of the solid is 10, what is the surface area of the solid?

A. 30
B. 33
C. 66
D. 86
E. 116

Given : lb(10)=30
lb=3
Assume, l=1 and b=3

Total surface area of a rectangle= 2(lb+bh+hl)
2(3+30+10) = 2*43= 86

IMO D
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Re: Each dimension of a rectangular solid is an integer less than 11. The [#permalink]
24 Nov 2020, 20:53
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