First, we need to calculate the total surface area of the cone to find the distance the ant would crawl. The formula for the surface area of a cone is:
Surface Area = πr(r + s),
where r is the radius of the base of the cone and s is the slant height.
Plugging in the values we have:
Surface Area = 3.14 * 20(20 + 29)
Surface Area = 3.14 * 20(49)
Surface Area = 3.14 * 980
Surface Area = 3077.2 mm2
Now, we need to find the circumference of the base of the cone, which the ant will crawl along to reach the top. The formula for the circumference of a circle is:
Circumference = 2πr
Plugging in the radius value:
Circumference = 2 * 3.14 * 20
Circumference = 125.6 mm
Therefore, the ant would crawl approximately 126 mm to get from the base of the cone to the top of the anthill.
An anthill has a volume of 8792 mm3 of dirt. Its radius is 20 mm. Its height is 21 mm and its slant is 29 mm. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. Use 3.14 for π and round your answer to the nearest millimeter if necessary.
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