Question

An edge of a variable sube is
e variable sebe is increasing at the rate 10cm/sec .How fast is the cube increasing
when the edge is 5cm
long​

Answer 1

Answer:

750cm^3/second

Step-by-step explanation:

given that

d(e)/dt=10cm/sec

we know that

v=e^3

differentiating on both sides

d(v)/dt=3e^2*d(e)/dt          (by applying chain rule)

we need to find the volume when e= 5cm

so ,

d(v)/dt=3*5^2 * de/dt

d(v)/dt=75*10

d(v)/dt=750 cm^3/sec

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Answer 2

Solution :

Let x be the length of the edge of the cube and v be its volume at any time t then

v = x³ and dx/dt = 10 cm/sec

now ,

v = x³

dv/dt = 3 x² dx/dt

dx/dt = 10

dv/dt = (3x²)(10)

dv/dt = 30x²

(dv/dt)_x = 5

= 30 (5)²

= 750 cm³sec

thus,

=> the volume of cube is increasing at the rate of 750 cm³/sec when the edge is 5 CM long