The radius r(t)r(t)r, (, t, )of a sphere is increasing at a rate of 7.57.57, point, 5 meters per minute. at a certain instant t_0t 0 t, start subscript, 0, end subscript, the radius is 555 meters. what is the rate of change of the surface area s(t)s(t)s, (, t, )of the sphere at that instant?

ds/dt=69743.35m^2/min

Step-by-step explanation:

The radius r(t)r(t)r, (, t, )of a sphere is increasing at a rate of 7.57.57, point, 5 meters per minute. At a certain instant t_0t 0 t, start subscript, 0, end subscript, the radius is 555 meters. What is the rate of change of the surface area S(t)S(t)S, (, t, )of the sphere at that instant?

If i could understand the question correctly, the typos notwithstanding

r=radius, 555m

dr/dt=rate of change in radius 5m/min

ds/dt=rate of change in surface area   ?

S=area of a sphere 4

ds/dt=ds/dr*dr/dt.................................1

ds/dr=differentiation of the area of a sphere=

ds/dt=*5

ds/dt=69743.35m^2/min

The surface area of the sphere will change by 69733.35 square meters for every minute.

v v cj van config k tbs eng r.c r.c fcb fb gb frfr

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: