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Direction: Consider the following for the next two (02) items:
The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
Q. If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?
The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
Q. If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?
- a)572 cm3
- b)728 cm3
- c)1144 cm3
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Direction: Consider the following for the next two (02) items:The sum ...
Let lengths, breadth and height of cuboid be l, b and h respectively
According to question
l+b+h = 22cm……(i)
and √(l2+b2+h2) = 14cm …..(ii)
S = l3+b3+h3 and V = lbh
S-3V = l3+b3+h3 - 3 lbh = (l+b+h)( l2+b2+h2-[lb+bh+lh])…(iii)
As we know
Squaring eq (i) gives
l2+b2+h2 + 2(lb+bh+lh) = 484
Substituting l2+b2+h2 from eq (i)
2(lb+bh+lh) = 484-196 = 288 cm2
lb+bh+lh = 144 cm2
Putting this in eq (iii) we get
22(196-144) = 22*52 = 1144cm2
According to question
l+b+h = 22cm……(i)
and √(l2+b2+h2) = 14cm …..(ii)
S = l3+b3+h3 and V = lbh
S-3V = l3+b3+h3 - 3 lbh = (l+b+h)( l2+b2+h2-[lb+bh+lh])…(iii)
As we know
Squaring eq (i) gives
l2+b2+h2 + 2(lb+bh+lh) = 484
Substituting l2+b2+h2 from eq (i)
2(lb+bh+lh) = 484-196 = 288 cm2
lb+bh+lh = 144 cm2
Putting this in eq (iii) we get
22(196-144) = 22*52 = 1144cm2
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Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Consider the following for the next two (02) items:The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.Q.If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?a)572 cm3b)728 cm3c)1144 cm3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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