The radius of a sphere increases at a rate of 4m/\sec. Find the rate at which the surface area increases when the radius is 9m. 288\pi m^{2}/\sec 36\pi m^{2}/\sec 18\pi m^{2}/\sec 72\pi m^{2}/\sec 144\pi m^{2}/\sec

preprekomW

preprekomW

Answered question

2021-05-04

The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area increases when the radius is 9m.
288πm2/sec
36πm2/sec
18πm2/sec
72πm2/sec
144πm2/sec

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-05-05Added 92 answers

Step 1
Surface area of sphere is S=4πr2.
And rate of change means derivatives.
Step 2
Now let radius of sphere is =r.
So dr/dt=4.
So rate of change of surface area =dS/dt=8πr.dr/dt=8π.9.4=288π.
So options A correct.

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