Question

Using the formula for volume of a cone, express r in terms of V, h and pi

Answer 1

The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,

    V = (1/3)(pi)(r^2)h         

Dividing both sides of the equation by (1/3)(pi)(h) will give us,

  3V/(pi)(h) = r^2

Taking the square-root of both sides,

  r = sqrt(3V/(pi)(h))

Answer 2

Answer:

$r = \sqrt{\displaystyle\frac{3V}{h\pi}}$

Step-by-step explanation:

We are given the following information in the question.

Using the formula for volume of cone, we have to express r in terms of V, h and pi.

Formula:

$\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}$

Now, we have to evaluate r, the radius of cone.

Rearranging the terms, we have,

Working:

$V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}$.

Thus, r in form of V, h and pi can be written as:

$r = \sqrt{\displaystyle\frac{3V}{h\pi}}$