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Tell whether the statement is true or false. Explain your reasoning The apothem of a regular polygon is always less than the radius.

A square is inscribed in a circle. The same square is also circumscribed about a smaller circle. Draw a diagram that represents this situation. Then id the ratio of the area of the larger circle to the area of the smaller circle.

REWRITING A FORMULA Write a formula in terms of the measure \(\theta\) (theta) of the central angle (in radians) that can be used to Ind the length of an arc of a circle. Then use this formula to Ind the length of an arc of a circle with a radius of 4 inches and a central angle of \(\frac{3 \pi}{4}\) radians.

The table shows how students get to school. $$\begin{array}{|c|c|}\hline \text { Method } & {\text { Percent of }} \text { students } \\ \hline \text { bus } & {65 \%} \\ {\text { walk }} & {25 \%} \\\ {\text { other }} & {10 \%} \\ \hline\end{array}$$ a. Explain why a circle graph is appropriate for the data. b. You will represent each method by a sector of a circle graph. Find the central angle to use for each sector. Then construct the graph using a radius of 2 inches. c. Find the area of each sector in your graph.

The outermost edges of the pattern shown form a square. If you know the dimensions of the outer square, is it possible to compute the total colored area? Explain.

Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. a. Find the volume of a tennis ball. b. Find the amount of space within the cylinder not taken up by the tennis balls.

A circular pizza with a 12 -inch diameter is enough for you and 2 friends. You want to buy pizzas for yourself and 7 friends. A 10 -inch diameter pizza with one topping costs \(\$ 6.99\) and a 14 -inch diameter pizza with one topping costs \(\$ 12.99 .\) How many 10 -inch and \(14-\) inch pizzas should you buy in each situation? Explain. a. You want to spend as little money as possible. b. You want to have three pizzas, each with a different topping, and spend as little money as possible. c. You want to have as much of the thick outer crust as possible.

MAKING AN ARGUMENT In the diagram, the measure of the red shaded angle is \(30^{\circ}\) . The arc length a is 2 . Your classmate claims that it is possible to and the circumference of the blue circle without Inding the radius of either circle. Is your classmate correct? Explain your reasoning.

PROBLEM SOLVING An aquarium shaped like a rectangular prism has a length of 30 inches, a width of 10 inches, and a height of 20 inches. You fill the aquarium \(\frac{3}{4}\) full with water. When you submerge a rock in the aquarium, the water level rises 0.25 inch. a. Find the volume of the rock. b. How many rocks of this size can you place in the aquarium before water spills out? a. Find the volume of the rock. b. How many rocks of this size can you place in the aquarium before water spills out?

PROBLEM SOLVING You drop an irregular piece of metal into a container partially filled with water and measure that the water level rises 4.8 centimeters. The square base of the container has a side length of 8 centimeters. You measure the mass of the metal to be 450 grams. What is the density of the metal?