For a hemisphere of radius [math]r[/math], determine a formula for the cross-sectional area created at height [math]h[/math] by the horizontal plane shown in the diagram.

[list=1] [*]Determine a formula for the radius [math]s[/math] of the circular cross section created at height [math]h[/math] of the hemisphere. [*]Use the resulting value for [math]s[/math] to find a formula for the area of the circular cross section shown in the diagram. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCSS Integrated Pathway Honors Supplement for Mathematics II[/i]. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.

A sugar-cube company makes sugar cubes in two sizes. Small sugar cubes have a side length of 1.0 cm and large sugar cubes have a side length of 1.5 cm. The company plans to expand its product line to include small and large sugar spheres, but the product manager does not want to change the actual amount of sugar in a small or large serving. Find a formula the company can use to determine the radius of a sugar cube with the same volume as a cube with side length [math]x[/math]. Then use the formula to advise the company’s product manager on the appropriate radii for the new sugar spheres.

[list=1] [*]Find a formula the company can use to determine the radius of a sugar sphere with the same volume as a sugar cube of side length [math]x[/math]. [*]Use the formula found in step 1 to determine the radii required for the proposed sugar spheres. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCSS Integrated Pathway Honors Supplement for Mathematics II[/i]. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.