Answer :
The rate at which the surface area decreases is -960 π m²/sec.
The surface area of a solid object is a measure of the entire vicinity that the floor of the object occupies. the distance occupied by means of a -dimensional flat surface is known as the area. it is measured in square devices. The location occupied through a three-dimensional item by using its outer surface is referred to as the surface place. it is also measured in square units.
The surface area is the full area included via all the faces of a 3D object. as an example, if we want to find the amount of paint required to paint a cube, then the floor on which the paint might be carried out is its surface vicinity. it is continually measured in rectangular units.
calculation:-
Given,
The radius of the sphere decreases at the rate of 6 m/ sec
mean dx/dt = -6
The surface area of the sphere of radius r is = 4πr²
Differentiating with respect to t,
dS/dt = 4π(2r)dx/dt
= 8πr dx/dt
dS/dt = 8π(20)²(-6)
= -960 π m²/sec
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