Question

A block of ice has a square top and bottom and rectangular sides. At a certain point in time each dimension of the square is 30cm and is decreasing at the rate of 2cm/h, while the depth is 20cm and decreasing at 3cm/h. How fast is the ice melting?

Answer 1

This is simple
the square surface area of ice melting per hour is = 2 X 2 = 4 cm^2
so the volume melting per hour is = 4 X 3 = 12 cm^3
This is the rate of melting of ice

Answer 2

That's what I thought as well, but it's not the right answer

Answer 3

i know how to solve but let me see how to explain it.....

Answer 4

original volume = l x b x h = 30 cm x 30 cm x 20 cm = 18000 cm^3

Answer 5

after one hour the l = 28 cm and b = 28 cm and h = 17 cm
new vol = 28 cm x 28 cm x 17 cm = 13328 cm^3

Decrease in vol = (18000-13328) cm^3 = 4672 cm^3 per hour

Answer 6

is this a calculus problem?

Answer 7

Harkirat, that's close but apparently the answer is -5100. I'm still not sure how to solve this. Yes, it's calculus. related rates

Answer 8

V=x^2y
dV = 2xy dx + x^2 dy

Answer 9

\[\frac{dV}{dt}=\frac{\partial V}{\partial x} \frac{dx}{dt}+\frac{\partial V}{\partial y} \frac{dy}{dt}\] where \[\frac{\partial V}{\partial x}=2xy\\\frac{\partial V}{\partial y}=x^2\\\frac{dx}{dt}=-2\\\frac{dy}{dt}=-3\]

Answer 10

How did you get the 2xy and the x^2?

Answer 11

\[\frac{\partial}{\partial x}\] means derivative with respect to x, when y is some constant.

here, \[\frac{\partial}{\partial x}(x^2y)=\text{derivative of x2 times the constant y}\]

Answer 12

and \[\frac{\partial}{\partial y}(x^2y)=\text{derivative of y times the constant x^2}=1(x^2)\]

Answer 13

Oh okay, that makes sense. Thank you so much!

Answer 14

yw