Question

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The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.

Write the formula to calculate the height, h.

Answer 1

The formula to calculate the height (h) of a cone, given its volume (V) and radius (r), is
`\(h = (3V)/(\pi r^2)\)`. This formula isolates the height by multiplying both sides of the volume formula by
`\(3/\pi r^2\).`

To isolate the height (h) in the volume formula of a cone (
`\(V = (1)/(3)\pi r^2 h\)`), we can rearrange the formula to solve for h.

Starting with the given formula:

`\[ V = (1)/(3)\pi r^2 h \]`

To find h, we can multiply both sides of the equation by
`\(3/\pi r^2\)` to isolate h:

`\[ h = (3V)/(\pi r^2) \]`

Therefore, the formula to calculate the height (h) of a cone, given its volume (V), radius (r), is:

`\[ h = (3V)/(\pi r^2) \]`

This formula allows you to determine the height of a cone when you know its volume and radius.

Answer 2

Explanation:

h=3V/IIr^2.

By using the change of subject of the formula, since V=1/3IIr^2h.

3 at the right hand side will multiply the volume V, then height h will be brought to the left hand side as the subject of the formula, which will now give h=3V/IIr^2.