The principal at Armstrong is buying candy for the freshman class. There are 210 students in the freshman class. If each box has 30 chocolate bars and each student can get 3 chocolate bars, about how many boxes should the principal buy?

he would need to buy 21 boxes of chocolate bars

Step-by-step explanation:

210 + 210 + 210 =630

630 divided by 30 equals 21

21 boxes. Hope this helped. <3

Step-by-step explanation:

  27.52 units

Step-by-step explanation:

The area of the 16-gon is 16 times the area of one of the sector triangles, so is ...

  16-gon area = 16×(1/2)bh = 8bh = 8(1.17 units)(2.94 units) = 27.5184 units²

  ≈ 27.52 units²

The circle area will be larger than the inscribed polygon and smaller than the circumscribing polygon. We have assumed the problem is describing an inscribed 16-gon, so the actual circle area can be estimated to be slightly larger than 27.52 units².

Comments on this answer and on the geometry

This is (presumably) the area of an inscribed 16-gon, so its area will be smaller than the area of the circumscribing circle.

We can figure the radius of the circle using the Pythagorean theorem:

  r² = h² +(b/2)² = (2.94 units)² +(0.585 units)² = 8.985825 units²

The area of the circumscribing circle is π times this, ...

  A = πr² ≈ 28.23 units²

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If we take the "height" of the sector to be the radius of the circle we are estimating, then the circle area is ...

  A = πr² = π(2.94 units)² ≈ 27.14 units² . . . . . . using 3.14 for π

Interestingly, this matches the smallest answer choice exactly. That is, the circle inscribed within the 16-gon has this area.

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Since a sector has a curved edge, we're not quite sure what the "base of one sector" is measuring. If it is 1/16 of the circumference of the circle, then the circle has an area of about 27.89 units². Then, we have no idea what the 2.94 is a measure of, since the circle's radius is 2.98 units. A 16-gon inscribed in this circle will have an apothem of 2.92 units.