Question

all edges of a cube are expending at a rate of 1cm/sec upon heating. calculate tha rate of increase of its volume and surface area when edge is 10 cm long
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Answer 1

→ Let the edge =x

Then volume V =x³

Hence DV/dt=3x²dx/dt

When x= 5 cm and dx/dt=10cm/sec

DV/dt=3×5²×10=750 cm³/sec

Hence rate of change of volume when x= 5 Cm and rate of change of x = 10 cm/sec=750 cm³/sec