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Sagot :
The rate at which the diameter decreases is -0.16cm/min
Diameter:
In geometry, diameter refers the straight line that goes from one side to the other side of a circle, passing through the center.
Given,
Here we need to find if a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm. Finish solving the problem. Write an equation that relates the quantities.
Here we obtained the equation that relates the surface area S and the diameter D of a sphere given by
=> S = πD²
Now, we have differentiate the equation as,
=> dS/dt = d/dt (πD²)
=> dS/dt = π d/dt (D²)
=> dS/dt = 2πD dD/dt
Now, Solving for dD/dt, which is the unknown for this problem, we have
=> dD/dt = 1/2πD x dS/dt
Now, substituting the given values, the rate of change of the diameter when D=10 cm and dS/dt as (-1) is
=> dD/dt = 1/2 x π x 10 (-1)
=> dD/dt = -1/20π
=> dD/dt = -0.16cm/min
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