Answer:
- 21 mm using the volume formula
- s is found using the Pythagorean theorem
- the ant crawls 29 mm
Explanation:
1.
The volume of a cone is given by the formula ...
V = 1/3πr²h
Filling in the given information, we can solve for the height.
8792 mm³ = 1/3π(20 mm)²h
Dividing by the coefficient of h, we find the height to be ...
h = 3(8792)/(3.14·400) mm = 21 mm
The height of the cone is 21 mm.
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2.
The slant height can be found using the Pythagorean theorem. It is the hypotenuse of a right triangle with legs equal to the radius (20 mm) and the height (21 mm).
s² = (20 mm)² +(21 mm)²
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3.
s² = (400 +441) mm² = 841 mm²
s = √(841 mm²) = 29 mm
The ant crawls 29 mm to get from the base of the hill to the top.