This question is worth 50 points, make sure to provide all calculations without using a calculator, though.

the local high school’s cheerleading squad is selling snow cones during lunch to raise money for a national cheerleading competition. paper cones are pre-filled with shaved ice and then filled with flavored syrup as customer orders are placed. the paper cones can contain no more than 535 cubic centimeters of shaved ice and syrup. if the paper cone is 8 centimeters deep, what is the largest width of the containers opening? use 3.14 to approximate . round your answer to the nearest whole unit. include all of your calculations in your final answer.

Step-by-step explanation:

Use the formula for the volume of a cone:

V = (1/3)(area of base / round opening)(height of cone)

In this case we're interested in the following:

(1/3)(area of base / round opening)(height of cone) ≤ 535 cm³

First, mult. both sides by 3 to elim. the fraction 1/3:

(area of base)(height) ≤ 1605 cm³

Since the height is 8 cm, we now have:

(area of base) / (8 cm) = 1605 cm³, or

(area of base) = (1605 cm³) · (8 cm) = 200.625 cm²

The formula for the area of a circle is A = 3.14·r², where r is the radius.

If the area of the base is 200.625 cm², as found above, this equals 3.14r², and so

r² = (200.625 cm²) / (3.14) = 63.89 cm²

Then the radius must be +√63.89 cm, or 8 cm

and the diameter must be 2r = 2(8 cm) = 16 cm.  This would be the largest width of the container.

what is the answer?