Question

3. How far does the ant crawl to get from the base of the cone to the top of the hill?

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Answer 1

The ant has to crawl an approximate distance of 29mm

Explanation:

Given

`Volume = 8792mm^3`

`r = 20mm` --- radius

See attachment

Required

Distance the ant has to crawl (i.e. the slant height)

First, we calculate the height of the hill

The volume of a cone is:

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

`8792 = (1)/(3) * (22)/(7) * 20^2*h`

`8792 = (1)/(3) * (22)/(7) * 400*h`

`8792 = (22* 400)/(3*7) *h`

Make h the subject

`h = (8792 * 3 * 7)/(22 * 400)`

`h = (184632)/(8800)`

`h = 20.98mm`

To calculate the slant height (s), we apply Pythagoras theorem

`s^2=h^2 + r^2`

`s^2=20.98^2 +20^2`

`s^2=840.1604`

`s=\sqrt{840.1604`

`s=28.9855205232`

`s= 29mm` --- approximated