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Is a given rectangular block a cube?
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.
- a)I alone sufficient while II alone not sufficient to answer
- b)II alone sufficient while I alone not sufficient to answer
- c)Either I or II alone sufficient to answer
- d)Both I and II are not sufficient to answer
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Is a given rectangular block a cube?I. At least 2 faces of the rectang...
From I, any two of l, b, h are equal.
From II, lbh = 64.
From I and II, the values of l, b, h may be (1, 1, 64), (2, 2, 16), (4, 4, 4).
Thus, the block may be a cube or cuboid.
∴ Correct answer is (d).
From II, lbh = 64.
From I and II, the values of l, b, h may be (1, 1, 64), (2, 2, 16), (4, 4, 4).
Thus, the block may be a cube or cuboid.
∴ Correct answer is (d).
Most Upvoted Answer
Is a given rectangular block a cube?I. At least 2 faces of the rectang...
Statement I: At least 2 faces of the rectangular block are squares.
Statement II: The volume of the block is 64.
To determine whether the given rectangular block is a cube, we need to consider both the statements together.
Statement I: At least 2 faces of the rectangular block are squares.
This statement alone is not sufficient to determine whether the given rectangular block is a cube. It only tells us that the block has at least 2 square faces, but it does not provide any information about the other faces or the dimensions of the block. A rectangular block can have more than 2 square faces and still not be a cube.
Statement II: The volume of the block is 64.
This statement alone is not sufficient to determine whether the given rectangular block is a cube. The volume of a rectangular block is calculated by multiplying its length, width, and height. While a volume of 64 can be achieved with a cube (e.g., if all the sides are 4 units long), it can also be achieved with different dimensions for a rectangular block (e.g., a block with dimensions 2 x 4 x 8 also has a volume of 64).
Combined statements:
Considering both statements together, we still cannot determine whether the given rectangular block is a cube. Statement I tells us that there are at least 2 square faces, but it does not provide any information about the other faces. Statement II tells us the volume of the block but does not provide any information about the dimensions of the block.
Therefore, both statements together are not sufficient to determine whether the given rectangular block is a cube. Hence, the correct answer is option D.
Statement II: The volume of the block is 64.
To determine whether the given rectangular block is a cube, we need to consider both the statements together.
Statement I: At least 2 faces of the rectangular block are squares.
This statement alone is not sufficient to determine whether the given rectangular block is a cube. It only tells us that the block has at least 2 square faces, but it does not provide any information about the other faces or the dimensions of the block. A rectangular block can have more than 2 square faces and still not be a cube.
Statement II: The volume of the block is 64.
This statement alone is not sufficient to determine whether the given rectangular block is a cube. The volume of a rectangular block is calculated by multiplying its length, width, and height. While a volume of 64 can be achieved with a cube (e.g., if all the sides are 4 units long), it can also be achieved with different dimensions for a rectangular block (e.g., a block with dimensions 2 x 4 x 8 also has a volume of 64).
Combined statements:
Considering both statements together, we still cannot determine whether the given rectangular block is a cube. Statement I tells us that there are at least 2 square faces, but it does not provide any information about the other faces. Statement II tells us the volume of the block but does not provide any information about the dimensions of the block.
Therefore, both statements together are not sufficient to determine whether the given rectangular block is a cube. Hence, the correct answer is option D.
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Is a given rectangular block a cube?I. At least 2 faces of the rectangular block are squares.II. The volume of the block is 64.a)I alone sufficient while II alone not sufficient to answerb)II alone sufficient while I alone not sufficient to answerc)Either I or II alone sufficient to answerd)Both I and II are not sufficient to answerCorrect answer is option 'D'. Can you explain this answer?
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