- #1
Physicsnoob90
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Homework Statement
The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions are ℓ = 4 m and
w = h = 9 m, and ℓ and w are increasing at a rate of 1 m/s while his decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing.
(A) The Volume
(B) The Surface Area
(C) the length of a diagonal (round two decimals places)
Homework Equations
The Chain rule, Partial Derivative
The Attempt at a Solution
I already found A (ans: -99 m^3/s) and B (ans: -94 m^2/s)
for C:
1. i differentiated the formula L^2= ℓ^2+w^2+h^2 to 2L(dL/dt) = 2ℓ(dℓ/dt) + 2w(dw/dt) + 2h (dh/dt)
2. let dℓ/dt = dw/dt = 1 m/s and dh/dt = -6 m/s
3. my answer came as 2L(dL/dt) = 82 but I'm completely lost after this part