Page 24 - How To Solve Word Problems In Calculus

is fixed so the maximum value of r occurs when x = 0.

2x + 2πr = 1
2πr = 1 (x = 0)

1
r =
2π

The area function and its domain are
1
A(r) = r − πr 2 0 ≤ r ≤
2π

Three–Dimensional Geometry Problems
Most three-dimensional word problems involve boxes, right
circular cylinders, spheres, and cones.
A box has a volume equal to the product of its length,
width, and height. The surface area of a closed box is the sum
of the areas of its six sides. An open box has no top; its volume
is the same as for a closed box, but its surface area involves
only five sides. A cube is a box whose edges are all equal.

Closed box V = lwh S = 2lw + 2lh + 2wh
Open box V = lwh S = lw + 2lh + 2wh
Cube V = s 3 S = 6s 2

V = lwh V = s 3
S = 2lw + 2lh + 2wh S = 6s 2

w s
h s

l s
A right circular cylinder of length h and radius r has volume
2
πr h and lateral surface area 2πrh. An easy way to remember
these is to multiply the area and circumference of a circle by h.

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