SOLUTION: A block of ice 8 in. and 5 in. by 3 in. is to be melted in an open conical pot 10 in deep and with radius 4 in. Find the depth of the water when the ice is completely melted in the

Algebra ->  Bodies-in-space -> SOLUTION: A block of ice 8 in. and 5 in. by 3 in. is to be melted in an open conical pot 10 in deep and with radius 4 in. Find the depth of the water when the ice is completely melted in the      Log On


   

Question 1021647: A block of ice 8 in. and 5 in. by 3 in. is to be melted in an open conical pot 10 in deep and with radius 4 in. Find the depth of the water when the ice is completely melted in the pot.
Found 2 solutions by Alan3354, FrankM:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A block of ice 8 in. and 5 in. by 3 in. is to be melted in an open conical pot 10 in deep and with radius 4 in. Find the depth of the water when the ice is completely melted in the pot.
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Volume = 8*5*3 = 120 cubic inches
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Vol of cone = pi%2Ar%5E2%2Ah%2F3+=+120
r/4 = h/10 --> r = 2h/5
pi%2A4%5E2%2Ah%2F3 --> pi%2A%282h%2F5%29%5E2%2Ah%2F3+=+120
pi%2A4h%5E3%2F75+=+120
h%5E3+=+9000%2F%284pi%29
h =~ 8.947 inches (if the point of the cone is at the bottom)

Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the ice block is 8*5*3=120 cu in.
for cone, V=1/3base*height and base is pi r^2
120=1/3 h * pi * 4^2
120 = 16/3 h * pi
120 * 3/16 = pi * h
22.5 = pi * h
h = 22.5 /3.1416
h= 7.16 in.
Note - this answer is correct for Math class, but not science class. When ice melts, it reduces in volume, about 9%. So a science teacher would expect you to take the 120 cu in and multiply by .91 before continuing.
I believe the other posted answer is not correct.
Vol of cone is 1/3 BH
The base is 16pi and my height is 7.16
(16*3.1416*7.16)/3 = 119.97 not 120 due to rounding.