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# A solid cube has side length 3 inches. A 2-inch by 2-inch square hole

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A solid cube has side length 3 inches. A 2-inch by 2-inch square hole  [#permalink]

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29 Mar 2019, 02:06
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Difficulty:

65% (hard)

Question Stats:

52% (02:47) correct 48% (02:33) wrong based on 25 sessions

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A solid cube has side length 3 inches. A 2-inch by 2-inch square hole is cut into the center of each face. The edges of each cut are parallel to the edges of the cube, and each hole goes all the way through the cube. What is the volume, in cubic inches, of the remaining solid?

(A) 7
(B) 8
(C) 10
(D) 12
(E) 15

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Re: A solid cube has side length 3 inches. A 2-inch by 2-inch square hole  [#permalink]

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29 Mar 2019, 03:05
1
Volume of the large cube= 27 cubic inches

The volume of the first hole across two opp faces = 2*2*3 ( square area* edge length)= 12 cubic inch

Two more pairs of such face to face hollows need to be considered by they will intersect with a common volume of an inner cube of 2*2*2 =8 cubic inch

Hence off the other 2 cut section for 2 opposite set of faces the remaining volume per cut piece= 12-8 = 4 cubic inch

Total volume remaining= 27(volume of large cube) - 8(Volume of Inner cube) - 3*4 (extra potion removed for each set of opposite faces) = 7 cubic inch

Ans: A
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Re: A solid cube has side length 3 inches. A 2-inch by 2-inch square hole  [#permalink]

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29 Mar 2019, 08:37
Bunuel wrote:
A solid cube has side length 3 inches. A 2-inch by 2-inch square hole is cut into the center of each face. The edges of each cut are parallel to the edges of the cube, and each hole goes all the way through the cube. What is the volume, in cubic inches, of the remaining solid?

(A) 7
(B) 8
(C) 10
(D) 12
(E) 15

good question
visualize and then solve
total volume of cube = 3^3 = 27
first cut ; 2*2*3 ; 12
second cut ; 2*2*.5 ; 2
third cut does the same as the second cut, on the last two faces. Hence the total volume of all cuts is 12 + 4 + 4 = 20
left vol ; 27-20; 7
IMO A
Re: A solid cube has side length 3 inches. A 2-inch by 2-inch square hole   [#permalink] 29 Mar 2019, 08:37
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