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All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the volume changing when each edge is 5 centimeter(s)

User Shockwave
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1 Answer

10 votes

Answer:

(a).The volume of cube is changing at the rate
450 cm^3/s

Explanation:

Let x be the side of cube


(dx)/(dt)=6 cm/s

We have to find the rate at which volume of cube changing when edge is 5 cm.

We know that

Volume of cube, V=
x^3

Differentiate w.r.t t


(dV)/(dt)=3x^2(dx)/(dt)

Substitute the values


(dV)/(dt)=3(5)^2* 6


(dV)/(dt)=450 cm^3/s

Hence, the volume of cube is changing at the rate
450 cm^3/s

User Jaggy
by
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