A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is π cm/s

Question

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is π cm/s (A) 0 (B) 2 (C) 8 (D) 9

Tardigrade Admin · Accepted Answer

v = (4/3)π r3 (dv/dt) = (4/3)π (d/dt)r3 = (4/3)π 3r2. (dr/dt) = 4π r2.(dr/dt) when r = 10 cm; (dv/dt) = 4π(10)2.(0.02)= 8 π cm3/s.

Q. A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of $0.02 c m / s$ . The rate of increase of its volume when the radius is $10 c m$ is ___________ $π$ cm/s

0

2

8

9

$v = \frac{4}{3} π r^{3}$
$\frac{d v}{d t} = \frac{4}{3} π \frac{d}{d t} r^{3} = \frac{4}{3} π 3 r^{2} . \frac{d r}{d t} = 4 π r^{2} . \frac{d r}{d t}$
when $r = 10 c m;$
$\frac{d v}{d t} = 4 π (10)^{2} . (0.02) = 8 π c m^{3} / s .$

Q. A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02cm/s. The rate of increase of its volume when the radius is 10cm is ___________π cm/s

0

2

8

9

v=34​πr3 dtdv​=34​πdtd​r3=34​π3r2.dtdr​=4πr2.dtdr​ when r=10cm; dtdv​=4π(10)2.(0.02)=8πcm3/s.

Q. A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of $0.02 c m / s$ . The rate of increase of its volume when the radius is $10 c m$ is ___________ $π$ cm/s

$v = \frac{4}{3} π r^{3}$
$\frac{d v}{d t} = \frac{4}{3} π \frac{d}{d t} r^{3} = \frac{4}{3} π 3 r^{2} . \frac{d r}{d t} = 4 π r^{2} . \frac{d r}{d t}$
when $r = 10 c m;$
$\frac{d v}{d t} = 4 π (10)^{2} . (0.02) = 8 π c m^{3} / s .$