<p>What is the volume of a prism whose bases are regular hexagons with sides of 4 and whose height is 10?</p>
<p>A. 200sqrt3
B. 240sqrt3
C. 360sqrt3
D. 480sqrt3
E. 600sqrt3</p>
<p>The answer is B. Please explain.</p>
<p>Nancy builds a fence around three sides of her rectangular vegetable garden. THe wall of her home forms the fourth side of the rectangle. If she uses 100 feet of fence, what is the maximum possible area(in square feet) of her garden? (Grid -in) </p>
<p>The answer is 1250. Pleas explain this too.</p>
<p>So volume of the prism will be the Height<em>Area of the hexagon. You know that a hexagon has 6 sides, and just treat the hexagon as 6 equilateral triangles meeting with sides of 4, and you get the area to be 24, and then times the height 10 and you get 240. If you look at it from the way of knowing the answer, the length(4)</em># of sides(6) *height(10) gets you that answer. </p>
<p>For the last one, we did a lot of these in our PreCalculus class where a graphing calculator comes in handy. Say the width is x(for both sides), so the length is 100-2x. Then you say that the area is x(100-2x), which gives you 100x-2x(^2). When you graph that on a graphing calculator, you see a parabola that opens up downwards, meaning that it has a maximum value for which it can't go higher(but it goes infinitely downward). I don't have a graphing calculator with me, but you get the idea.</p>