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Observe the following statements
I) If the radius of spherical ball is increased by $\frac{1}{2} %$ then approximate increase in volume is 1%
II) In measuring the radius and height of a cone as 5 cm, 10 cm there are errors 0.02 cm, 0.01 cm respectively. Then error in volume approximately is $2.25 π c . c$ Correct statement is

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only I

only II

both I and II

neither I nor II

answer is D.

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Detailed Solution

$i) \frac{δ r}{r} \times 100 = \frac{1}{2}, v = \frac{4}{3} π r^{3} \frac{δ v}{v} = 3 \cdot \frac{δ r}{r}$

$ii) r = 5, h = 10 cm, δ r = 0.02, δ h = 0.01$

$\Rightarrow v = \frac{1}{3} π r^{2} h \Rightarrow δ v = \frac{π}{3} [2 r h δ r + π r^{2} δ h]$

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