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A cube of edge 3 cm is cut into smaller cubes of edge 1 cm. The ratio of the total surface area of all the smaller cubes to the surface area of the larger cube is equal to:
- a)1 : 3
- b)3 : 1
- c)1 : 1
- d)2 : 9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A cube of edge 3 cm is cut into smaller cubes of edge 1 cm. The ratio ...
Surface area of cube of side 1cm = 6 x 1 * 1 = 6 cm2 Number of cubes of side 1 cm = 27
Total surface area of all small cubes = 27 x 6 cm2 Surface area of the larger cube = 6 * 3 x 3 = 9 x 6 cm2
Required ratio = (27 x 6) : (9 x 6) = 3 : 1
Total surface area of all small cubes = 27 x 6 cm2 Surface area of the larger cube = 6 * 3 x 3 = 9 x 6 cm2
Required ratio = (27 x 6) : (9 x 6) = 3 : 1
Most Upvoted Answer
A cube of edge 3 cm is cut into smaller cubes of edge 1 cm. The ratio ...
Surface area of cube of side 1cm = 6 x 1 * 1 = 6 cm2 Number of cubes of side 1 cm = 27
Total surface area of all small cubes = 27 x 6 cm2 Surface area of the larger cube = 6 * 3 x 3 = 9 x 6 cm2
Required ratio = (27 x 6) : (9 x 6) = 3 : 1
Total surface area of all small cubes = 27 x 6 cm2 Surface area of the larger cube = 6 * 3 x 3 = 9 x 6 cm2
Required ratio = (27 x 6) : (9 x 6) = 3 : 1
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A cube of edge 3 cm is cut into smaller cubes of edge 1 cm. The ratio ...
Solution:
Let's start by finding the surface area of the larger cube.
The surface area of a cube is given by the formula: A = 6s^2, where s is the length of the side of the cube.
In this case, the length of the side of the larger cube is 3 cm. So the surface area of the larger cube is:
A = 6(3^2) = 6(9) = 54 cm^2
Now let's find the total surface area of all the smaller cubes.
The number of smaller cubes that can be formed from the larger cube is given by the formula: (s1/s2)^3, where s1 is the length of the side of the larger cube and s2 is the length of the side of the smaller cube.
In this case, s1 = 3 cm and s2 = 1 cm. So the number of smaller cubes that can be formed is:
(3/1)^3 = 3^3 = 27
Each smaller cube has a surface area of 6(1^2) = 6 cm^2.
Therefore, the total surface area of all the smaller cubes is:
27 * 6 = 162 cm^2
Now we can find the ratio of the total surface area of all the smaller cubes to the surface area of the larger cube:
Ratio = (total surface area of all smaller cubes) / (surface area of larger cube) = 162 cm^2 / 54 cm^2 = 3 : 1
So the correct answer is option B: 3 : 1.
Let's start by finding the surface area of the larger cube.
The surface area of a cube is given by the formula: A = 6s^2, where s is the length of the side of the cube.
In this case, the length of the side of the larger cube is 3 cm. So the surface area of the larger cube is:
A = 6(3^2) = 6(9) = 54 cm^2
Now let's find the total surface area of all the smaller cubes.
The number of smaller cubes that can be formed from the larger cube is given by the formula: (s1/s2)^3, where s1 is the length of the side of the larger cube and s2 is the length of the side of the smaller cube.
In this case, s1 = 3 cm and s2 = 1 cm. So the number of smaller cubes that can be formed is:
(3/1)^3 = 3^3 = 27
Each smaller cube has a surface area of 6(1^2) = 6 cm^2.
Therefore, the total surface area of all the smaller cubes is:
27 * 6 = 162 cm^2
Now we can find the ratio of the total surface area of all the smaller cubes to the surface area of the larger cube:
Ratio = (total surface area of all smaller cubes) / (surface area of larger cube) = 162 cm^2 / 54 cm^2 = 3 : 1
So the correct answer is option B: 3 : 1.
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A cube of edge 3 cm is cut into smaller cubes of edge 1 cm. The ratio of the total surface area of all the smaller cubes to the surface area of the larger cube is equal to:a)1 : 3b)3 : 1c)1 : 1d)2 : 9Correct answer is option 'B'. Can you explain this answer?
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