Question

The volume of a cube is increasing at the rate of 9 cm cube per second how fast is its surface area increasing

Answer 1

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The volume of a cube is increasing at the rate of 9cm/sec. How fast is the Surface Area increasing when the length of an edge is10cm?

Answer:-

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The answer is in the attachment. When the length of an edge is 10 cm then the rate of Surface Area increase is 3.6cm²/s.

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Answer 2

The surface area is increasing at the rate 3.6 cm square per second.

Step-by-step explanation:

We are given the following in the question:

The volume of a cube is increasing at the rate of 9 cm cube per second.

$\dfrac{dV}{dt} = 9$

Volume of cube is given by

$V = s^3\\\\\dfrac{dV}{dt} = \dfrac{d(s^3)}{st} = 3s^2\dfrac{ds}{dt} = 9\\\\\dfrac{ds}{dt} = \dfrac{3}{s^2}$

Edge of cube,s = 10 cm

Surface area of cube =

$S =6s^2$

Rate of increase in surface area =

$\dfrac{dS}{dt} = \dfrac{d(6s^2)}{dt}\\\\\dfrac{dS}{dt} = 12s\dfrac{ds}{dt}\\\\\dfrac{dS}{dt} = 12s\times \dfrac{3}{s^2} = 12\times \dfrac{3}{10}\\\\\dfrac{dS}{dt} = 3.6$

Thus, the surface area is increasing at the rate 3.6 cm square per second.

#LearnMore

The volume of a cube is increasing at a constant rate . Prove that the increase in surface area varies inversely as the length of the cube.

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