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Two cylinder of length 2.5m and 15m are to be cut into equal pieces without leaving any extra length of cylinder. Find the greatest length of the cylinder pieces of same size which can be cut from these two
- a)25 m
- b)75 m
- c)2.5 m
- d)15 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two cylinder of length 2.5m and 15m are to be cut into equal pieces wi...
Maximum length of each piece
= HCF of 2.5m and 15in = 2.5m
Required size = 2.5 m
= HCF of 2.5m and 15in = 2.5m
Required size = 2.5 m
Most Upvoted Answer
Two cylinder of length 2.5m and 15m are to be cut into equal pieces wi...
To find the greatest length of the cylinder pieces that can be cut from two cylinders of lengths 2.5m and 15m, we need to find the greatest common divisor (GCD) of the two lengths. The GCD will represent the length of each piece that can be cut from both cylinders without leaving any extra length.
To calculate the GCD, we can use the Euclidean algorithm:
1. Find the remainder when the larger length is divided by the smaller length.
- 15m ÷ 2.5m = 6m remainder 0
2. If the remainder is 0, then the smaller length is the GCD.
- In this case, the GCD is 2.5m.
Therefore, the greatest length of the cylinder pieces that can be cut from both cylinders is 2.5m.
Let's go through the options provided:
a) 25m: This is not a possible length since it exceeds the length of both cylinders.
b) 75m: This is not a possible length since it exceeds the length of both cylinders.
c) 2.5m: This is the correct answer. The GCD of 2.5m and 15m is 2.5m, which represents the maximum length of the cylinder pieces that can be cut from both cylinders without any extra length.
d) 15m: This is not a possible length since it exceeds the length of the smaller cylinder (2.5m).
Therefore, option 'C' (2.5m) is the correct answer.
In conclusion, the greatest length of the cylinder pieces that can be cut from two cylinders of lengths 2.5m and 15m is 2.5m, as determined by finding the GCD of the two lengths.
To calculate the GCD, we can use the Euclidean algorithm:
1. Find the remainder when the larger length is divided by the smaller length.
- 15m ÷ 2.5m = 6m remainder 0
2. If the remainder is 0, then the smaller length is the GCD.
- In this case, the GCD is 2.5m.
Therefore, the greatest length of the cylinder pieces that can be cut from both cylinders is 2.5m.
Let's go through the options provided:
a) 25m: This is not a possible length since it exceeds the length of both cylinders.
b) 75m: This is not a possible length since it exceeds the length of both cylinders.
c) 2.5m: This is the correct answer. The GCD of 2.5m and 15m is 2.5m, which represents the maximum length of the cylinder pieces that can be cut from both cylinders without any extra length.
d) 15m: This is not a possible length since it exceeds the length of the smaller cylinder (2.5m).
Therefore, option 'C' (2.5m) is the correct answer.
In conclusion, the greatest length of the cylinder pieces that can be cut from two cylinders of lengths 2.5m and 15m is 2.5m, as determined by finding the GCD of the two lengths.
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