Question

The volume of a cube is increasing at the rate of 8cm3/.How fast is the surface area increasing when the length of an edge is 12 cm ?​

Answer 1

Answer:

Hint- In order to solve this type of question, we must know the concept of differentiation. Also we must know the chain rule as we have to find the area with the given length.

⇒ Volume of a cube =x3

⇒Surface area =6x2

Complete step-by-step answer:

Let x be the length of the side, v be the volume and s be the surface area of a cube.

Here we are given that

⇒dvdt=8cm3 per second.

Then by using the chain rule,

We get

⇒8=dvdt=dx3dt×dxdx

Or 8 = 3x2×dxdt

⇒dxdt=83x2 ……………………………………………(1)

Now, we will solve dsdt,

⇒d(6x2)dt=d(6x2)dt×dxdx=d(6x2)dx×dxdt=12x×dxdt

We used chain rule to solve the above mentioned equation.

⇒12x ×dxdt

⇒ 12x ×83x2

⇒ 32x

Thus using the given condition,

When x = 12 cm

⇒dsdt = 3212cm2per second

⇒83 cm2 per second is the right answer.

∴ Hence if the length of the edge of the cube is

Answer 2

Answer:

refer to the attachment

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Step-by-step explanation:

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