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12 Dec 2018, 01:36
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
49% (01:58) correct
51%
(02:07)
wrong
based on 160
sessions
History
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Time
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Not Attempted Yet
A cube of white chalk is painted red and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids is not painted red.
A. 15%
B. 16 2/3%
C. 20%
D. 25%
E. 33 1/3%
A. 15%
B. 16 2/3%
C. 20%
D. 25%
E. 33 1/3%
Updated on: 12 Dec 2018, 01:51
Originally posted by EgmatQuantExpert on 12 Dec 2018, 01:49.
Last edited by EgmatQuantExpert on 12 Dec 2018, 01:51, edited 1 time in total.
Last edited by EgmatQuantExpert on 12 Dec 2018, 01:51, edited 1 time in total.
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Solution
Given:
- • A cube of white chalk is painted red and then cut parallel to the sides to form two rectangular solids of equal volume.
To find:
- • The percent of the surface area of each of the new solids not painted red.
Approach and Working:
Let us assume that each side of the cube is of n units length.
- • Hence, total surface area of the cube = surface area of the red faces = \(6 * n^2\)
If it is cut into half, then each piece will have red surface area of \(3n^2\) (half of \(6n^2\)) and one white surface, which is of area \(n * n = n^2\)
- • Total surface area of each piece = \(3n^2 + n^2 = 4n^2\)
Therefore, the percent of surface area of each cube which is not red = \(\frac{n^2}{4n^2} * 100\)= 25%
Hence, the correct answer is option D.
Answer: D
12 Dec 2018, 01:50
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Bunuel
let the cube be of side 4 each so total volume of cube 64
supposedly now if we cut the cube horizontally then rectangle then length would still be 4 but breadth will become 2 ; for the two halves of the cube on each side we would get 4 rectangles and 1 square
TSA of 1 half of side : 4* { 2 ( 4+2)} + 4*4 = 48+16= 64 ,since there are two sides so TSA of painted side would be 64 * 2 = 128
now the side which is not painted would be a square whose surface area is 4*4 = 16 since there are 2 such sides so 2*16 = 32
% of side not painted : 32/128 = 25% IMO D
