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If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.
- a)20 cm2/s
- b)40 cm2/s
- c)70 cm2/s
- d)30 cm2/s
Correct answer is option 'D'. Can you explain this answer?
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If the circumference of the circle is changing at the rate of 5 cm/s t...
The circumference of the circle is given by C=2πr, where r is the radius of the circle.
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If the circumference of the circle is changing at the rate of 5 cm/s t...
To find the rate of change of the area of a circle, we need to use the formula for the area of a circle and differentiate it with respect to time.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius is 6 cm and the circumference is changing at a rate of 5 cm/s, we can use the formula for the circumference of a circle to find the rate of change of the radius.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Differentiating this equation with respect to time, we get dC/dt = 2π(dr/dt).
Given that dC/dt = 5 cm/s, we can solve for dr/dt.
5 cm/s = 2π(dr/dt)
dr/dt = 5 cm/s / (2π)
dr/dt ≈ 0.7957 cm/s
So, the rate of change of the radius is approximately 0.7957 cm/s.
Next, we can differentiate the formula for the area of a circle with respect to time to find the rate of change of the area.
dA/dt = d(πr^2)/dt
Using the chain rule, we can differentiate this equation as follows:
dA/dt = 2πr(dr/dt)
Substituting the given values, we have:
dA/dt = 2π(6)(0.7957)
dA/dt ≈ 30 cm^2/s
Therefore, the rate of change of the area of the circle is approximately 30 cm^2/s. Hence, the correct answer is option 'D'.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius is 6 cm and the circumference is changing at a rate of 5 cm/s, we can use the formula for the circumference of a circle to find the rate of change of the radius.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Differentiating this equation with respect to time, we get dC/dt = 2π(dr/dt).
Given that dC/dt = 5 cm/s, we can solve for dr/dt.
5 cm/s = 2π(dr/dt)
dr/dt = 5 cm/s / (2π)
dr/dt ≈ 0.7957 cm/s
So, the rate of change of the radius is approximately 0.7957 cm/s.
Next, we can differentiate the formula for the area of a circle with respect to time to find the rate of change of the area.
dA/dt = d(πr^2)/dt
Using the chain rule, we can differentiate this equation as follows:
dA/dt = 2πr(dr/dt)
Substituting the given values, we have:
dA/dt = 2π(6)(0.7957)
dA/dt ≈ 30 cm^2/s
Therefore, the rate of change of the area of the circle is approximately 30 cm^2/s. Hence, the correct answer is option 'D'.
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If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer?
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If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer?.
If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer?.
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If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.a)20 cm2/sb)40 cm2/sc)70 cm2/sd)30 cm2/sCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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