Question

an anthill has a volume of 8792mm^3 of dirt. its radius is 20 mm. what is the height of the cone? explain how you found the height.​

Answer 1

Height, h = 21 millimeters.

Explanation:

Given the following data;

Volume = 8792mm³

Radius = 20 mm

To find the height;

We know that the shape of an anthill is conical in nature.

Mathematically, the volume of a cone is given by the formula;

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

Where;

• V is the volume of the cone.
• r is the radius of the base of the cone.
• h is the height of the cone.

Substituting into the equation, we have;

`8792 = (1)/(3) * 3.142*20^(2)*h`

`8792 = (1)/(3) * 3.142*400*h`

`8792 = (1)/(3) * 1256.8*h`

`8792 = 418.93*h`

`Height, h = \frac {8792}{418.93}`

Height, h = 20.99 ≈ 21 mm.

Therefore, the height of the cone is 21 millimeters.