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If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be: [2008]
- a)4%
- b)6%
- c)8%
- d)2%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the error in the measurement of radius of a sphere is 2%, then the ...
Error in the measurement of radius of a sphere = 2%
Volume of the sphere = 
∴ Error in the volume = 
= 3 × 2% = 6%
Most Upvoted Answer
If the error in the measurement of radius of a sphere is 2%, then the ...
To understand why the error in the measurement of the radius of a sphere affects the determination of its volume, we need to understand the relationship between the radius and the volume of a sphere.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
Let's consider the error in the measurement of the radius as a percentage. The error in the radius is given as 2% or 0.02.
Now, let's calculate the error in the determination of the volume of the sphere.
**Calculating the Error in the Volume:**
To find the error in the volume, we need to consider how the error in the radius affects the volume formula.
The formula for the volume of a sphere is V = (4/3)πr^3. Taking the derivative of this formula with respect to r, we get dV/dr = 4πr^2.
Now, let's calculate the relative error in the volume (ΔV/V), which is the ratio of the error in the volume (ΔV) to the actual volume (V).
(ΔV/V) = (dV/dr * Δr) / V
(ΔV/V) = (4πr^2 * Δr) / [(4/3)πr^3]
(ΔV/V) = (3 * Δr) / r
Substituting the given error in the radius (Δr = 0.02) into the equation, we get:
(ΔV/V) = (3 * 0.02) / r
(ΔV/V) = 0.06 / r
From the above equation, we can see that the relative error in the volume is directly proportional to the error in the radius (Δr).
**Conclusion:**
Since the relative error in the volume is 0.06/r, the error in the determination of the volume of the sphere will be 6% when the error in the measurement of the radius is 2%.
Therefore, the correct answer is option B) 6%.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
Let's consider the error in the measurement of the radius as a percentage. The error in the radius is given as 2% or 0.02.
Now, let's calculate the error in the determination of the volume of the sphere.
**Calculating the Error in the Volume:**
To find the error in the volume, we need to consider how the error in the radius affects the volume formula.
The formula for the volume of a sphere is V = (4/3)πr^3. Taking the derivative of this formula with respect to r, we get dV/dr = 4πr^2.
Now, let's calculate the relative error in the volume (ΔV/V), which is the ratio of the error in the volume (ΔV) to the actual volume (V).
(ΔV/V) = (dV/dr * Δr) / V
(ΔV/V) = (4πr^2 * Δr) / [(4/3)πr^3]
(ΔV/V) = (3 * Δr) / r
Substituting the given error in the radius (Δr = 0.02) into the equation, we get:
(ΔV/V) = (3 * 0.02) / r
(ΔV/V) = 0.06 / r
From the above equation, we can see that the relative error in the volume is directly proportional to the error in the radius (Δr).
**Conclusion:**
Since the relative error in the volume is 0.06/r, the error in the determination of the volume of the sphere will be 6% when the error in the measurement of the radius is 2%.
Therefore, the correct answer is option B) 6%.
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Community Answer
If the error in the measurement of radius of a sphere is 2%, then the ...
Volume of sphere = 4/3 π r³
Error = 3 ×∆r / r ×100
= 3×2
= 6%
Error = 3 ×∆r / r ×100
= 3×2
= 6%
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If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be: [2008]a)4%b)6%c)8%d)2%Correct answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be: [2008]a)4%b)6%c)8%d)2%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be: [2008]a)4%b)6%c)8%d)2%Correct answer is option 'B'. Can you explain this answer?.
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