When the radius of a sphere decreases from $3 c m$ to $2.98 c m$ then the approximately decrease in volume of sphere is
$0.72 π {cm}^{3}$
$0.008 π {cm}^{3}$
$0.072 π {cm}^{3}$
$0.002 π {cm}^{3}$

Question

When the radius of a sphere decreases from 3 cm to 2-98 cm then the approximately decrease in volume of sphere is0-72pi  text-cm-3-0-008pi  text-cm-3-0-072pi  text-cm-3-0-002pi  text-cm-3-

Toppr Admin · Accepted Answer

Given radius of sphere decreases from 3 cm to 2.98 cm
volume of sphere $= \frac{4}{3} π r^{3}$
$△ r = r_{2} - r_{1}$
$= 2.98 - 3$
$△ r = - 0.02$
$d r = - 0.02$
consider $y = \frac{4}{3} π r^{3}$
$\frac{d y}{d r} = \frac{4}{3} π 3 r^{2}$
$\frac{d y}{d r} = 4 π r^{2}$
$d y = 4 π r^{2} . d r$
$d y = 4 π 3^{2} . (- 0.02)$
$d y = 4 (3.14) 9 (- 0.02)$
$d y = 36 π (- 0.02)$
$d y = - 0.72 π c m^{3}$
$∴$ The volume of sphere
decrease by $- 0.72 π c m^{3}$

When the radius of a sphere decreases from 3 cm to 2.98 cm then the approximately decrease in volume of sphere is0.72π cm30.008π cm30.072π cm30.002π cm3

Given radius of sphere decreases from 3 cm to 2.98 cmvolume of sphere =43πr3△r=r2−r1=2.98−3△r=−0.02dr=−0.02consider y=43πr3dydr=43π3r2dydr=4πr2dy=4πr2.drdy=4π32.(−0.02)dy=4(3.14)9(−0.02)dy=36π(−0.02)dy=−0.72πcm3∴ The volume of spheredecrease by −0.72πcm3

When the radius of a sphere decreases from $3 c m$ to $2.98 c m$ then the approximately decrease in volume of sphere is
$0.72 π {cm}^{3}$
$0.008 π {cm}^{3}$
$0.072 π {cm}^{3}$
$0.002 π {cm}^{3}$