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A cube of white chalk is painted red and then cut parallel to the side

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Bunuel
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A cube of white chalk is painted red and then cut parallel to the side [#permalink] New post   12 Dec 2018, 01:36
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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%
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D
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EgmatQuantExpert
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A cube of white chalk is painted red and then cut parallel to the side [#permalink] New post   Updated on: 12 Dec 2018, 01:51
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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


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.
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Re: A cube of white chalk is painted red and then cut parallel to the side [#permalink] New post   12 Dec 2018, 01:50
Bunuel wrote:
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%



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
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Re: A cube of white chalk is painted red and then cut parallel to the side [#permalink] New post   17 Mar 2020, 01:28
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Bunuel wrote:
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%



Assume the cube has each side of length 1.
Then total surface area of the cube is 6*(1)^2 = 6 (all painted surface area)

When you cut it into two, half the painted surface area (3) is taken by each solid and one new surface is created on each solid. This new surface is a square with side 1 so area of 1^2 = 1

Unpainted area/ Total = 1/(3 + 1) = 25%

Answer (D)
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Re: A cube of white chalk is painted red and then cut parallel to the side [#permalink] New post   15 Jan 2022, 11:31
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Re: A cube of white chalk is painted red and then cut parallel to the side [#permalink]
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