Question

1. What is the height of the cone? Explain how you found the height.

2. Now that you have the height of the cone, how can you solve for the slant height, s?

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

Answer 1

1. 21 mm using the volume formula
2. s is found using the Pythagorean theorem
3. 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.