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Two identical cubes each of total surface area of 6 cm2 are joined end to end. Which of thefollowing is the total surface area of the cuboid so formed?
- a)12 cm2
- b)18 cm2
- c)10 cm2
- d)8 cm2
Correct answer is option 'C'. Can you explain this answer?
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Two identical cubes each of total surface area of 6 cm2 are joined end...
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- c)10 cm2
Step-by-step explanation:
CUBOID
l=2
b=1
h=1
TSA =2(2+1+2)
=2�5
ANS ; 10
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Two identical cubes each of total surface area of 6 cm2 are joined end...
To find the total surface area of the cuboid formed by joining two identical cubes, we need to first determine the dimensions of the cuboid.
Let's assume that the length of each side of the cube is 'a'. Therefore, the total surface area of each cube is given by 6a² (since a cube has 6 faces, and each face has an area of a²).
Since we are joining the two cubes end to end, the length of the cuboid will be equal to the sum of the lengths of the two cubes, which is 2a.
The width and height of the cuboid will be equal to the length of each side of the cube, which is a.
Therefore, the dimensions of the cuboid formed are:
Length = 2a
Width = a
Height = a
Now, let's calculate the total surface area of the cuboid.
Total Surface Area of a cuboid = 2 (Length × Width + Length × Height + Width × Height)
Substituting the values, we get:
Total Surface Area = 2 (2a × a + 2a × a + a × a)
= 2 (2a² + 2a² + a²)
= 2 (5a²)
= 10a²
Since the total surface area of each cube is 6 cm², we can equate it to 10a² and solve for 'a'.
6 = 10a²
Dividing both sides by 10, we get:
0.6 = a²
Taking the square root of both sides, we get:
a ≈ 0.775
Now, substituting the value of 'a' in the equation for the total surface area, we get:
Total Surface Area ≈ 10 × (0.775)²
≈ 10 × 0.6
≈ 6 cm²
Therefore, the total surface area of the cuboid formed by joining two identical cubes is 6 cm².
Let's assume that the length of each side of the cube is 'a'. Therefore, the total surface area of each cube is given by 6a² (since a cube has 6 faces, and each face has an area of a²).
Since we are joining the two cubes end to end, the length of the cuboid will be equal to the sum of the lengths of the two cubes, which is 2a.
The width and height of the cuboid will be equal to the length of each side of the cube, which is a.
Therefore, the dimensions of the cuboid formed are:
Length = 2a
Width = a
Height = a
Now, let's calculate the total surface area of the cuboid.
Total Surface Area of a cuboid = 2 (Length × Width + Length × Height + Width × Height)
Substituting the values, we get:
Total Surface Area = 2 (2a × a + 2a × a + a × a)
= 2 (2a² + 2a² + a²)
= 2 (5a²)
= 10a²
Since the total surface area of each cube is 6 cm², we can equate it to 10a² and solve for 'a'.
6 = 10a²
Dividing both sides by 10, we get:
0.6 = a²
Taking the square root of both sides, we get:
a ≈ 0.775
Now, substituting the value of 'a' in the equation for the total surface area, we get:
Total Surface Area ≈ 10 × (0.775)²
≈ 10 × 0.6
≈ 6 cm²
Therefore, the total surface area of the cuboid formed by joining two identical cubes is 6 cm².
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Two identical cubes each of total surface area of 6 cm2 are joined end to end. Which of thefollowing is the total surface area of the cuboid so formed?a)12 cm2b)18 cm2c)10 cm2d)8 cm2Correct answer is option 'C'. Can you explain this answer?
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