Latest Microsoft Aptitude Question SOLUTION: A cube whose edge is 20 cm long has circleon each of its face painted black. what is the total area of unpainted surface of the cube if the cicles are of largest possible area ? (a

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A cube whose edge is 20 cm long has circleon each of its face painted black. what is the total area of unpainted surface of the cube if the cicles are of largest possible area ?
(a) 85.71 cm2 (b) 257.14 cm2
(c) 514.28 cm2 (d) 331.33 cm2

Asked In Microsoft sahil (8 years ago)

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Tanmayi Joshi  (8 years ago)

total area of one side of cube = 20*20 = 400 cm2
circle area = 3.14 * 10 * 10 = 314 cm2 (Since the circle is largest as possible. Therefore, diameter= 20 and radius = 10)
unpainted area of one side of cube = 400-314 = 86cm2
since cube has 6 faces. Therefore, the total area of unpainted region = 6*86 = 516 cm2

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Suraj  (8 years ago)

Option C)
The radius of the largest possible circle on the face of a cube will be 10 cm.
Area of the circle = 22/7*10*10 = 314.2857 sq.cm.
Total area of a face = 20*20= 400 sq.cm.
Now the unpainted area on a face = 400 -314.2857=85.7143 sq.cm.
Total unpainted area on 6 faces = 6*85.7143 = 514.28 sq.cm.

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Siddhartha Bokaria  (8 years ago)

6*a^2 - 6*((a/2)^2)*(22/7) = surface area unpainted
6*400 - 6*100*3.14
2400 - 1884 = 516cm2

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Seth  (6 years ago)

Circle occupying maximum area inside a square is by having it's radius equal to half the length of side of the square. So here the radius of the circle will be 10cm. Area of square of length 20cm is 400cm. A cube of 20cm length will have 6 square faces of length 20cm. Area of circle of 10cm is 3.1416*10*10 = 314.16. The unoccupied on a square face area will be 400 - 314.16 = 85.84. Since there are 6 such faces, there will be six leftover spaces. Total leftover space is 6*85.84 = 515.04 which is nearer to 514.28(resulted due to precision).

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priyadarsini  (8 years ago)

C) 514.28cm2

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SHIVAM SHUKLA  (8 years ago)

c : 514.28

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tejaswi A  (8 years ago)

c)514.28 cm2
explanation:-6*(20*20-3.14*10*10)

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K Ronith Raj  (6 years ago)

radius of circle =10cm.
area = 3.1417*10*10=314.17
20*2-314.17=85.83
85.83*6=514.98

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Siba Prasad Mohanty  (6 years ago)

Let's consider 1 side of a cube. Area of 1 side= 400cm^2
Maximum area of Circle in 1 side=3.14*10*10=314cm^2
So, Area left uncovered= 400-314=86cm^2
Hence, total area of 6 faces= 86*6=516cm^2

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rahul  (5 years ago)

6*20*20-6*20*20/4*3.13

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Shubham Bansal  (4 years ago)

Total Surface area of cube = 6 X 20 X 20 = 2400 Sqcm
Diameter of largest possible circle = Edge of cube i.e. 20 cm
Area of all circles = 6 X 3.14 X 10 X 10 = 1884 Sqcm
Area of unpainted surface = 2400 - 1884 = 516 Sqcm
The nearest value to 516 is 514.28.

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