3. A spherical piece of ice is melting. While melting, its radius is decreasing

Question

3. A spherical piece of ice is melting. While melting, its radius is decreasing a constant rate of 0.1 inches per minute. How fast is the volume decreasing whe the radius is 3 inches? 4. Suppose the ice from the previous problem is suspended above a conical paper up measuring 8 inches across the top and 6 inches deep. As the ice melts, the water drips into the cup. When the radius of the ice is 3 inches, the height of the water in the cup is 4 inches. Assuming a constant melt rate, how fast is the water in the cup rising?

Explanation / Answer

3. A spherical piece of ice is melting. While melting, its radius is decreasing a constant rate of 0.1 inches per minute. How fast is the volume decreasing whe the radius is 3 inches?

first consider the volume of sphere

V = 4/3 pi r^3

now take derivative

dv/dt = 4/3 *pi*3 r^2 dr/dt

given r = 3 in

dr/dt = 0.1 inch permin

dv/dt = 4*pi*3^2*0.1 = 11.30973355292326 inc^3 per min

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