Math, asked by cobyproctor2, 1 year ago

A block of ice has a square top and bottom and rectangular sides. At a certain point in time, the square top and bottom each have a length of 30cm, which are decreasing at 2cm/h. At the same time, the height of the block is 20 cm and decreasing at 3cm/h. How fast is the ice melting?

Answers

Answered by Anonymous
9

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Answer

Let s be the length of the square sides and let r be the length of the rectangular side, the "depth" as you worded it.

The volume of the ice is given by:

V = s²r

You want to find dV/dt. Use product rule:

dV/dt = 2sr*ds/dt + s²*dr/dt

s = 30 cm

r = 20 cm

ds/dt = -2 cm/hr

dr/dt = -3 cm/hr

Now just insert the values and calculate dV/dt:

dV/dt = 2(30)(20)(-2) + (30²)(-3)

dV/dt = -2400 + -2700

dV/dt = -5100 cm³/hr


rohitkumargupta: nice
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