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Which of the following is case of direct variation:
- a)If the length of radius is increased the circumference will be increased
- b)If number of students is a hostel are increased then the fixed food provision will last forless days
- c)For fixed duration, more the periods, lesser will be the duration of one period
- d)In case of a cylindrical vessel, lesser the diameter more is the level of water in it.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following is case of direct variation:a)If the length of ...
Direct Variation
Direct variation is a mathematical relationship between two variables in which an increase in one variable leads to a proportional increase in the other variable. In other words, as one variable increases, the other variable also increases by a constant ratio.
Options:
a) If the length of radius is increased, the circumference will be increased.
b) If the number of students in a hostel is increased, then the fixed food provision will last for fewer days.
c) For a fixed duration, the more the periods, the lesser will be the duration of one period.
d) In the case of a cylindrical vessel, the lesser the diameter, the more is the level of water in it.
Explanation:
Among the given options, the case of direct variation is described in option 'A'.
Explanation of Option 'A':
If the length of the radius is increased, the circumference will be increased.
- When we talk about a circle, the circumference is the distance around the circle, and the radius is the distance from the center of the circle to any point on its boundary.
- The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
- In this case, if the length of the radius is increased, the value of 'r' in the formula will increase, leading to an increase in the value of 'C'.
- This shows that as the radius increases, the circumference also increases, and the two variables are directly proportional to each other.
- The constant ratio between the radius and the circumference is 2π, which means that for every increase in the radius by a certain amount, the circumference will increase by 2π times that amount.
Conclusion:
Option 'A' is a case of direct variation because an increase in the length of the radius leads to a proportional increase in the circumference of a circle.
Direct variation is a mathematical relationship between two variables in which an increase in one variable leads to a proportional increase in the other variable. In other words, as one variable increases, the other variable also increases by a constant ratio.
Options:
a) If the length of radius is increased, the circumference will be increased.
b) If the number of students in a hostel is increased, then the fixed food provision will last for fewer days.
c) For a fixed duration, the more the periods, the lesser will be the duration of one period.
d) In the case of a cylindrical vessel, the lesser the diameter, the more is the level of water in it.
Explanation:
Among the given options, the case of direct variation is described in option 'A'.
Explanation of Option 'A':
If the length of the radius is increased, the circumference will be increased.
- When we talk about a circle, the circumference is the distance around the circle, and the radius is the distance from the center of the circle to any point on its boundary.
- The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
- In this case, if the length of the radius is increased, the value of 'r' in the formula will increase, leading to an increase in the value of 'C'.
- This shows that as the radius increases, the circumference also increases, and the two variables are directly proportional to each other.
- The constant ratio between the radius and the circumference is 2π, which means that for every increase in the radius by a certain amount, the circumference will increase by 2π times that amount.
Conclusion:
Option 'A' is a case of direct variation because an increase in the length of the radius leads to a proportional increase in the circumference of a circle.
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Which of the following is case of direct variation:a)If the length of radius is increased the circumference will be increasedb)If number of students is a hostel are increased then the fixed food provision will last forless daysc)For fixed duration, more the periods, lesser will be the duration of one periodd)In case of a cylindrical vessel, lesser the diameter more is the level of water in it.Correct answer is option 'A'. Can you explain this answer?
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Which of the following is case of direct variation:a)If the length of radius is increased the circumference will be increasedb)If number of students is a hostel are increased then the fixed food provision will last forless daysc)For fixed duration, more the periods, lesser will be the duration of one periodd)In case of a cylindrical vessel, lesser the diameter more is the level of water in it.Correct answer is option 'A'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Which of the following is case of direct variation:a)If the length of radius is increased the circumference will be increasedb)If number of students is a hostel are increased then the fixed food provision will last forless daysc)For fixed duration, more the periods, lesser will be the duration of one periodd)In case of a cylindrical vessel, lesser the diameter more is the level of water in it.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is case of direct variation:a)If the length of radius is increased the circumference will be increasedb)If number of students is a hostel are increased then the fixed food provision will last forless daysc)For fixed duration, more the periods, lesser will be the duration of one periodd)In case of a cylindrical vessel, lesser the diameter more is the level of water in it.Correct answer is option 'A'. Can you explain this answer?.
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