91Ó°ÊÓ

OPEN-ENDED Sketch two rectangular prisms that have volumes of 100 cubic inches but different surface areas. Include dimensions in your sketches.

A spherical lune is the region between two great circles of a sphere. Find the formula for the area of a lune.

Explain how to find the area of the regular hexagon by dividing the hexagon into equilateral triangles.

Rewrite the formula for the area of a rhombus for the special case of a square with side length s. Show that this is the same as the formula for the area of a square, \(A=s^{2}\)

Use the formula for the area of a regular polygon to show that the area of an equilateral triangle can be found by using the formula \(A=\frac{1}{4} s^{2} \sqrt{3},\) where \(s\) is the side length.

CRITICAL THINKING The height of cylinder X is twice the height of cylinder Y. The radius of cylinder X is half the radius of cylinder Y. Compare the volumes of cylinder X and cylinder Y. Justify your answer.

MATHEMATICAL CONNECTIONS You drill a circular hole of radius r through the base of a cylinder of radius R. Assume the hole is drilled completely through to the other base. You want the volume of the hole to be half the volume of the cylinder. Express r as a function of R.

Solve the triangle. Round decimal answers to the nearest tenth. $$\mathrm{B}=102^{\circ}, \mathrm{C}=43^{\circ}, \mathrm{b}=21$$

ANALYZING RELATIONSHIPS How can you change the edge length of a cube so that the volume is reduced by 40%?

The area of a regular n-gon is given by \(A=\frac{1}{2} a P\) . As n approaches in infinity, what does the n-gon approach? What does \(P\) approach? What does a approach? What can you conclude from your three answers? Explain your reasoning.