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THIS ANSWER IS CORRECT RIGHT?

If a snowball melts so that its surface area decreases at a rate of 0.3 cm²/min, find the rate at which the diameter decreases when the diameter is 18 cm.

(Answer: -0.00026525)

Isn’t this the right answer? My college webwork system is so messed up it never takes the correct thing!

User Vilarix
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1 Answer

5 votes

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.

User Shelby L Morris
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