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17 April, 18:56

A hypothetical cube grows so that the length of its sides are increasing at a rate of 2 m/min. How fast is the volume of the cube increasing when the sides are 8m each?

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  1. 17 April, 19:15
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    In a min the volume increased by 296m^3

    Step-by-step explanation:

    Volume of cube = v^3

    At 8m = V = 8*8*8 = 512

    Since it's growing at 2m/min

    The previous volume A min ago would have been

    8m - 2m = 6m

    V = 6*6*6 = 216

    So in a minute, the volume had gone from 216 to 512

    The speed = 512 - 216 = 296

    So it's volume increased by 296 in a min.

    Just for future clarification.

    (2 min ago the volume would have been.

    8m - (2*2) m = 4

    V 2min ago = 4*4*4 = 64.

    At 2mins ago the volume changed by 216 - 64 = 152.

    So this is what the volume looked like Each minute

    0, 8, 64, 216, 512, 1000.)
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