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The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height?
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The radio of two cylinder are in the ratio 1:under root 3 if the volum...
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The radio of two cylinder are in the ratio 1:under root 3 if the volum...
Ratio of Radii
Let's assume the ratio of the radii of the two cylinders is 1:x. According to the given information, this ratio is equal to 1:√3.
So, we can write the equation:
1/x = 1/√3
To simplify the equation, we can rationalize the denominator:
1/x = √3/3
Cross-multiplying, we get:
√3 * x = 1 * 3
√3 * x = 3
Squaring both sides of the equation:
(√3 * x)^2 = 3^2
3x^2 = 9
Dividing both sides by 3:
x^2 = 3
Taking the square root of both sides:
x = √3
Therefore, the ratio of the radii of the two cylinders is 1:√3.
Ratio of Heights
Now, let's assume the ratio of the heights of the two cylinders is y:1.
The volume of a cylinder is given by the equation:
Volume = π * r^2 * h
Since the volume of the two cylinders is the same, we can write the equation:
π * 1^2 * y = π * (√3)^2 * 1
Simplifying the equation:
y = 3
Therefore, the ratio of the heights of the two cylinders is 3:1.
Final Answer
The ratio of the respective heights of the two cylinders is 3:1.
Let's assume the ratio of the radii of the two cylinders is 1:x. According to the given information, this ratio is equal to 1:√3.
So, we can write the equation:
1/x = 1/√3
To simplify the equation, we can rationalize the denominator:
1/x = √3/3
Cross-multiplying, we get:
√3 * x = 1 * 3
√3 * x = 3
Squaring both sides of the equation:
(√3 * x)^2 = 3^2
3x^2 = 9
Dividing both sides by 3:
x^2 = 3
Taking the square root of both sides:
x = √3
Therefore, the ratio of the radii of the two cylinders is 1:√3.
Ratio of Heights
Now, let's assume the ratio of the heights of the two cylinders is y:1.
The volume of a cylinder is given by the equation:
Volume = π * r^2 * h
Since the volume of the two cylinders is the same, we can write the equation:
π * 1^2 * y = π * (√3)^2 * 1
Simplifying the equation:
y = 3
Therefore, the ratio of the heights of the two cylinders is 3:1.
Final Answer
The ratio of the respective heights of the two cylinders is 3:1.
Community Answer
The radio of two cylinder are in the ratio 1:under root 3 if the volum...
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The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height?
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The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height?.
The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radio of two cylinder are in the ratio 1:under root 3 if the volume of two cylinder be same find the ratio of their respective height?.
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