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A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.
- a)106π cm2
- b)144π cm2
- c)186π cm2
- d)196π cm2
- e)256π cm2
Correct answer is option 'D'. Can you explain this answer?
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A balloon, which always remains spherical, has a variable radius. Find...
To find the rate at which the volume of the balloon is increasing with respect to its radius, we can use the formula for the volume of a sphere:
V = (4/3)πr^3
Where V is the volume and r is the radius. To find the rate of change of volume with respect to the radius, we can take the derivative of the volume formula with respect to r:
dV/dr = (4/3)π(3r^2)
Now, we can substitute the radius value of 7 cm into the derivative formula to find the rate of change of volume with respect to the radius when the radius is 7 cm:
dV/dr = (4/3)π(3(7)^2)
= (4/3)π(3(49))
= (4/3)π(147)
= 196π
Therefore, the rate at which the volume of the balloon is increasing with respect to its radius when the radius is 7 cm is 196π.
V = (4/3)πr^3
Where V is the volume and r is the radius. To find the rate of change of volume with respect to the radius, we can take the derivative of the volume formula with respect to r:
dV/dr = (4/3)π(3r^2)
Now, we can substitute the radius value of 7 cm into the derivative formula to find the rate of change of volume with respect to the radius when the radius is 7 cm:
dV/dr = (4/3)π(3(7)^2)
= (4/3)π(3(49))
= (4/3)π(147)
= 196π
Therefore, the rate at which the volume of the balloon is increasing with respect to its radius when the radius is 7 cm is 196π.
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A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer?
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A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer?.
A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with respect to its radius, when the radius is 7 cm.a)106π cm2b)144π cm2c)186π cm2d)196π cm2e)256π cm2Correct answer is option 'D'. Can you explain this answer?.
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