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

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 = 1 m, and ℓ and w are increasing at a rate of 8 m/s while h is decreasing at a rate of 2 m/s. At that instant find the rates at which the following quantities are changing.

(a) The volume.

(b) The surface area.

Solutions

Expert Solution

Solution-

a.)

The volume of the box is given by,

Rate of change of volume with respect to time,

Substitute,

(b)

The surface area is given by,

Rate of change for Area is given by,

substitute from the first part,

(c) Length of diagonal can be written as,

rate of change for the length of diagonal,

substitute from the first part,

milcah answered 1 year ago

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