Answer:
The ant has to crawl an approximate distance of 29mm
Step-by-step explanation:
Given
[tex]Volume = 8792mm^3[/tex]
[tex]r = 20mm[/tex] --- 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:
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
[tex]8792 = \frac{1}{3} * \frac{22}{7} * 20^2*h[/tex]
[tex]8792 = \frac{1}{3} * \frac{22}{7} * 400*h[/tex]
[tex]8792 = \frac{22* 400}{3*7} *h[/tex]
Make h the subject
[tex]h = \frac{8792 * 3 * 7}{22 * 400}[/tex]
[tex]h = \frac{184632}{8800}[/tex]
[tex]h = 20.98mm[/tex]
To calculate the slant height (s), we apply Pythagoras theorem
[tex]s^2=h^2 + r^2[/tex]
[tex]s^2=20.98^2 +20^2[/tex]
[tex]s^2=840.1604[/tex]
[tex]s=\sqrt{840.1604[/tex]
[tex]s=28.9855205232[/tex]
[tex]s= 29mm[/tex] --- approximated
Answer:
The ant has to crawl an approximate distance of 29mm
Step-by-step explanation:
