Answer:
<h2>
16 cm</h2>
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.
