Question

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Answer 1

Answer:

correct answer is option number b

Step-by-step explanation:

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Answer 2

It is 4 : 3

Step-by-step explanation:

Let the radius and height of the cylinder are the same and it is x.

So, the volume of the cylinder, $V_1 = \pi x^{3}$

Now, differentiating the above equation with respect to x we get the rate of change of volume, i.e.

$\frac{dV_1}{dx} = 3\pi x^{2}$ ............ (1)

Again, the volume of a sphere with radius x is given by $V_2 = \frac{4}{3}\pi x^{3}$.

Now, differentiating the above equation with respect to x we get the rate of change of volume, i.e.

$\frac{dV_2}{dx} = \frac{4}{3} \pi (3x^{2}) = 4\pi x^{2}$ .............. (2)

Therefore, from equations (1) and (2) we get the ratio of the rate of change of volume of the sphere to the rate of change of volume of the cylinder is

4πx² : 3πx² = 4 : 3 (Answer)