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?
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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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