SOLUTION: An ice "cube" is in the shape of a rectangular prism. As the ice"cube" melts the relationship between the edges remains constant. The base of the ice "cube" is square and its heigh

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Question 909409: An ice "cube" is in the shape of a rectangular prism. As the ice"cube" melts the relationship between the edges remains constant. The base of the ice "cube" is square and its height is half of its width. The initial width is 30mm and as the ice "cube" melts its width decreases at a rate of 4mm per hour. Determine the instantaneous rate of change in the volume of the ice cube at 1 hour. Include a graph.
I would really appreciate help with this question, Thank you so much!
(not sure if I put it in the correct category, couldn't find one for instantaneous rate of change)
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
An ice "cube" is in the shape of a rectangular prism. As the ice"cube" melts the relationship between the edges remains constant. The base of the ice "cube" is square and its height is half of its width. The initial width is 30mm and as the ice "cube" melts its width decreases at a rate of 4mm per hour. Determine the instantaneous rate of change in the volume of the ice cube at 1 hour. Include a graph.
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Get the volume in terms of the width.
Vol = w^3/2
differentiate wrt t
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dV/dt = 3w^2/2*dw/dt
At 1 hr, w = 26 mm
= 3*26^2*4/2
dV/dt = 4056 cubic mm/hr