G: Geometry

Geometry

Example Problems

Convert the angle

\theta = -30^\circ

to radians.
Express your answer exactly.

There is exactly one reflection and no rotation that sends the convex quadrilateral

ABCD

onto itself. What shape(s) could quadrilateral

ABCD

be? Explain.

A gymnastics team uses a hemispherical chalk bowl with a radius of

7.5\text{ cm}

.

What is the capacity of the chalk bowl?
Round to the nearest cubic centimeter.

Consider the complex number:

z = i

What is

z^{11}

?

About how many cells are in the human body?
(You can assume that a cell is a sphere with radius

10^{-3}\text{ cm}

and that the density of a cell is approximately the density of water, which is

1\text{ g/cm}^3

.)

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