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The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 300% respectively. Then the increase in the volume of the cuboid is
- a)5 times
- b)6 times
- c)12 times
- d)17 times
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3....
Suppose length, breadth and height of cuboid are respectively x, 2x, 3x
∴ Volume of cuboid = x x 2x x 3x = 6x3
Now, increased length, breadth, height of cuboid
= x x 200/100 , 2x x 300/100 , 3x x 300 /100 = 2x, 6x, 9x
∴ Volume of new cuboid = 2x x 6x 9x = 108x3
Increase in volume of cuboid = (108 - 6)x3 = 102 x3 = 6x3 x 17
= 17 times the original volume.
∴ Volume of cuboid = x x 2x x 3x = 6x3
Now, increased length, breadth, height of cuboid
= x x 200/100 , 2x x 300/100 , 3x x 300 /100 = 2x, 6x, 9x
∴ Volume of new cuboid = 2x x 6x 9x = 108x3
Increase in volume of cuboid = (108 - 6)x3 = 102 x3 = 6x3 x 17
= 17 times the original volume.
Most Upvoted Answer
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3....
Solution:
Let the length, breadth and height of the cuboid be x, 2x and 3x respectively.
Original volume of the cuboid = x × 2x × 3x = 6x³
After increase in dimensions, new length = 2x + 100% of 2x = 4x
New breadth = 2(2x) + 200% of 2x = 8x
New height = 3(3x) + 300% of 3x = 12x
New volume of the cuboid = 4x × 8x × 12x = 384x³
Increase in volume = New volume - Original volume = 384x³ - 6x³ = 378x³
Increase in volume in terms of original volume = (378x³/6x³) = 63
Therefore, the increase in volume of the cuboid is 63 times the original volume which is option D (17 times).
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Let the length, breadth and height of the cuboid be x, 2x and 3x respectively.
Original volume of the cuboid = x × 2x × 3x = 6x³
After increase in dimensions, new length = 2x + 100% of 2x = 4x
New breadth = 2(2x) + 200% of 2x = 8x
New height = 3(3x) + 300% of 3x = 12x
New volume of the cuboid = 4x × 8x × 12x = 384x³
Increase in volume = New volume - Original volume = 384x³ - 6x³ = 378x³
Increase in volume in terms of original volume = (378x³/6x³) = 63
Therefore, the increase in volume of the cuboid is 63 times the original volume which is option D (17 times).
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Solution:
Let the length, breadth and height of the cuboid be x, 2x and 3x respectively.
Original volume of the cuboid = x × 2x × 3x = 6x³
After increase in dimensions,
- New length = 2x + 100% of 2x = 4x
- New breadth = 2(2x) + 200% of 2x = 8x
- New height = 3(3x) + 300% of 3x = 12x
New volume of the cuboid = 4x × 8x × 12x = 384x³
Increase in volume = New volume - Original volume = 384x³ - 6x³ = 378x³
Increase in volume in terms of original volume = (378x³/6x³) = 63
Therefore, the increase in volume of the cuboid is 63 times the original volume which is option D (17 times).
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The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 300% respectively. Then the increase in the volume of the cuboid isa)5 timesb)6 timesc)12 timesd)17 timesCorrect answer is option 'D'. Can you explain this answer?
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