Answer:
NO
Explanation:
The surface area of a sphere can be expressed as:
A = 4πr^2
where r is the radius of the sphere. We can express the radius in terms of the diameter as:
r = d/2
where d is the diameter.
Differentiating both sides of the surface area equation with respect to time t gives:
dA/dt = 8πr (dr/dt)
where dr/dt is the rate of change of the radius with respect to time.
We are given that the surface area is decreasing at a rate of 0.3 cm²/min, so we have:
dA/dt = -0.3 cm²/min
We are also given that the diameter is 18 cm, so we can find the radius as:
r = d/2 = 9 cm
Substituting these values into the equation above gives:
-0.3 = 8π(9) (dr/dt)
Solving for dr/dt gives:
dr/dt = -0.3 / (8π(9)) = -0.001326 cm/min
Therefore, the rate at which the diameter is decreasing when the diameter is 18 cm is approximately 0.001326 cm/min.