Question

An anthill has a volume of 8792 mm3 of dirt. Its radius is 20 mm. How far does an ant have to crawl to get from the base of the cone to the top of the hill? (This is the
slant height, s, of the cone.) Answer the questions to find out.

Answer 1

Answer:

The slope is 29 mm.

Step-by-step explanation:

What we know:

The radius of this cone is 20 mm, and the height is 21mm

s = √r^2 + h^2

s = √20^2 + 21^2

s = √400 + 441

s = √841

s = 29 mm

Answer 2

The slant height of the cone is required,

The ant would have to crawl $29\ \text{mm}$

Volume of cone

V = Volume of cone = $8792\ \text{mm}^3$

r = Radius of cone = 20 mm

h = Height

s = Slant height.

Volume of a cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\Rightarrow h=\dfrac{3V}{\pi r^2}\\\Rightarrow h=\dfrac{3\times 8792}{3.14\times 20^2}\\\Rightarrow h=21\ \text{mm}$

From Pythagoras theorem we have

$s=\sqrt{r^2+h^2}\\\Rightarrow s=\sqrt{20^2+21^2}\\\Rightarrow s=29\ \text{mm}$

Learn more about slant height:

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