The volume of a cube is increasing at a rate of 10 cm^3/min . How fast is the surface area increasing when the length of an edge is 3.0 cm?
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Answer:
Surface area of the cube is increasing at a rate of 49 cm2min
Explanation:
If the length of an edge of a cube is l cm.,
its volume V is l3 and surface area A is 6l2.
Differentiating V=l3 w.r.t. time, we get
dVdt=3l2dldt
As dVdt=10 cm3min, wen l=90
dldt=103×902=12430
As A=6l2
dAdt=12l×dldt=12×90×12430=49 cm2min
Surface area of the cube is increasing at a rate of 49 cm2min
Explanation:
If the length of an edge of a cube is l cm.,
its volume V is l3 and surface area A is 6l2.
Differentiating V=l3 w.r.t. time, we get
dVdt=3l2dldt
As dVdt=10 cm3min, wen l=90
dldt=103×902=12430
As A=6l2
dAdt=12l×dldt=12×90×12430=49 cm2min
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The volume of a cube is increasing at a rate of 10 cm^3 per min. How fast is the surface area increasing when the length of an edge is .
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