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The dimensions of a cuboid are 8 cm × 4 cm × 27 cm. How many cubes of side 2 cm can be made by melting the cuboid?
- a)160
- b)155
- c)169
- d)108
Correct answer is option 'D'. Can you explain this answer?
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The dimensions of a cuboid are 8 cm × 4 cm × 27 cm. How ma...
Let the no. of cubes of side a that can be made by melting the given cuboid = n
Total volume of these cubes = na3
Total volume of all the smaller cubes is equal to the volume of the original cube
As a = 2
⇒ 8 cm × 4 cm × 27 cm = 23 × n
⇒ n = 108
Most Upvoted Answer
The dimensions of a cuboid are 8 cm × 4 cm × 27 cm. How ma...
Calculating the Number of Cubes:
To find out how many cubes of side 2 cm can be made by melting the given cuboid, we need to first calculate the volume of the cuboid.
Finding the Volume of the Cuboid:
The volume of a cuboid is given by the formula: V = l × b × h, where l is the length, b is the breadth, and h is the height of the cuboid.
Given dimensions:
Length (l) = 8 cm
Breadth (b) = 4 cm
Height (h) = 27 cm
Therefore, the volume of the cuboid = 8 cm × 4 cm × 27 cm = 864 cm³
Calculating the Number of Cubes:
Now, we need to find out how many cubes of side 2 cm can be made from the volume of the cuboid. Since each cube has a side length of 2 cm, the volume of each cube is 2 cm × 2 cm × 2 cm = 8 cm³.
To find the total number of cubes that can be made, we divide the volume of the cuboid by the volume of each cube:
Total number of cubes = 864 cm³ ÷ 8 cm³ = 108 cubes
Therefore, the correct answer is option D) 108 cubes.
To find out how many cubes of side 2 cm can be made by melting the given cuboid, we need to first calculate the volume of the cuboid.
Finding the Volume of the Cuboid:
The volume of a cuboid is given by the formula: V = l × b × h, where l is the length, b is the breadth, and h is the height of the cuboid.
Given dimensions:
Length (l) = 8 cm
Breadth (b) = 4 cm
Height (h) = 27 cm
Therefore, the volume of the cuboid = 8 cm × 4 cm × 27 cm = 864 cm³
Calculating the Number of Cubes:
Now, we need to find out how many cubes of side 2 cm can be made from the volume of the cuboid. Since each cube has a side length of 2 cm, the volume of each cube is 2 cm × 2 cm × 2 cm = 8 cm³.
To find the total number of cubes that can be made, we divide the volume of the cuboid by the volume of each cube:
Total number of cubes = 864 cm³ ÷ 8 cm³ = 108 cubes
Therefore, the correct answer is option D) 108 cubes.
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The dimensions of a cuboid are 8 cm × 4 cm × 27 cm. How many cubes of side 2 cm can be made by melting the cuboid?a)160b)155c)169d)108Correct answer is option 'D'. Can you explain this answer?
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