Question

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

Answer 1

Answer:

The ant has to crawl an approximate distance of 29mm

Step-by-step 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:

$Volume = \frac{1}{3}\pi r^2h$

$8792 = \frac{1}{3} * \frac{22}{7} * 20^2*h$

$8792 = \frac{1}{3} * \frac{22}{7} * 400*h$

$8792 = \frac{22* 400}{3*7} *h$

Make h the subject

$h = \frac{8792 * 3 * 7}{22 * 400}$

$h = \frac{184632}{8800}$

$h = 20.98mm$

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