
The length, breadth and height of cuboid are in the ratio 1:2:3. If they are increased by 100%, 200% and 200% respectively, then, as compared to the original volume the increase in the volume of the cuboid will be:
A. 5 times
B. 18 times
C. 12 times
D. 17 times
Answer
527.4k+ views
Hint: Take the proportionate as ‘x’. thus get the length, breadth and height of the original cuboid. Then find l,b & h, new, increased side. Then find the volume of the original cuboid and new increased volume of the cuboid. Subtract them to find the increases in volume of cuboid.
Complete step-by-step answer:
We have been given a cuboid whose length, breadth and height in the ratio 1:2:3. Now let us take ‘x’ as the side.
The length of cuboid .
The breadth of cuboid .
The height of cuboid .
Now their dimensions of the cuboid are increased by 100%, 200% and 200%. i.e. the length of cuboid is increased by 100%, the breadth is increased by 200% and the height is increased by 200%.
Hence, the new dimensions of the cuboid are
Length .
Breadth .
Height .
Hence, the original dimensions of cuboid .
New dimensions of the cuboid .
We know that volume of a cuboid .
Original volume of cuboid
Now increased volume of cuboid
Thus the increase in volume = New increased volume – original volume of cuboid
Thus we can write the increase in volume as,
We know that is the original value.
Increase in volume
Thus, when comparing the original volume the increase in the volume of cuboid is 17 times.
Option (D) is the correct answer.
Note: It is said length, breadth and height are in ratio. Don’t take different variables for the 3 quantities as l,b,h etc. take as they are in proportionate as ‘x’. putting 3 variables is complicated and you won't get the answer.
Complete step-by-step answer:
We have been given a cuboid whose length, breadth and height in the ratio 1:2:3. Now let us take ‘x’ as the side.
The breadth of cuboid
The height of cuboid
Now their dimensions of the cuboid are increased by 100%, 200% and 200%. i.e. the length of cuboid is increased by 100%, the breadth is increased by 200% and the height is increased by 200%.
Hence, the new dimensions of the cuboid are
Length
Breadth
Height
Hence, the original dimensions of cuboid
New dimensions of the cuboid
We know that volume of a cuboid
Now increased volume of cuboid
Thus the increase in volume = New increased volume – original volume of cuboid
Thus we can write the increase in volume as,
We know that
Thus, when comparing the original volume the increase in the volume of cuboid is 17 times.
Note: It is said length, breadth and height are in ratio. Don’t take different variables for the 3 quantities as l,b,h etc. take as they are in proportionate as ‘x’. putting 3 variables is complicated and you won't get the answer.
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