Volume of a cone = 1/3 πr squared h where r is the radius and h the height the volume of the cone below is 800cm cubed calculate height of cone

Question

asked Mar 10, 2024 232k views

1 Answer

Evgeniy Berezovsky · Answer 1 · 2024-03-14T09:10:13+0000

To calculate the height of the cone, we can rearrange the formula for the volume of a cone:

$\displaystyle\sf V = (1)/(3) \pi r^2 h$

Given that the volume
$\displaystyle\sf V$ is 800 cm³, we can substitute this value into the equation:

$\displaystyle\sf 800 = (1)/(3) \pi r^2 h$

To isolate
$\displaystyle\sf h$ , we can divide both sides of the equation by
$\displaystyle\sf (1)/(3) \pi r^2$ :

$\displaystyle\sf (800)/((1)/(3) \pi r^2) = h$

Simplifying the expression on the right side:

$\displaystyle\sf h = (3 \cdot 800)/(\pi r^2)$

Therefore, the height of the cone is given by
$\displaystyle\sf (3 \cdot 800)/(\pi r^2)$ .