Question

the height of a rectangular box is 10 in. Its length increases at the rate of 2 in/sec.;its width decreases at the rate of 4 in/sec. When the length is 8 in and the width is 6 in, the volume of the box is changing in cubic inches per second at the rate of ?
A 200
B 80
C -80
D -200
E -20

Answer 1

i got -200 but wasn't sure

Answer 2

v = 10xy
dv/dt = 10(y dx/dt + x dy/dt)

So, using your numbers,

dv/dt = 10(8(-4) + 6(2)) = -200

looks good to me.

Answer 3

ty!