The length l , width w , and height h of a box change with time. At a certain in

Question

The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 5 m and w = h = 4 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume.
m3/s

(b) The surface area.
m2/s

(c) The length of a diagonal. (Round the answer to two decimal places.)
m/s
The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 5 m and w = h = 4 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume.
m3/s

(b) The surface area.
m2/s

(c) The length of a diagonal. (Round the answer to two decimal places.)
m/s The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 5 m and w = h = 4 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume.
m3/s

(b) The surface area.
m2/s

(c) The length of a diagonal. (Round the answer to two decimal places.)
m/s (a) The volume.
m3/s

(b) The surface area.
m2/s

(c) The length of a diagonal. (Round the answer to two decimal places.)
m/s

Explanation / Answer

let x be the rat in m/s at which the length of each side is changing.

Volume= (5+(3x))*(4+(3x))*(4-(6x))

Surface Area= 2(((5+(3x))*(4+(3x)))+((4+(3x))*(4-(6x)))+((4-(6x))+(5+(3x)))

Diagonnal= sqrt(((5+(3x))^2)+((4+(3x))^2)+(4-(6x))^2))

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