The drinking glass is in cylinder shape.

Surface area of the drinking glass is $\"\"$ square inches

Formula for the surface area of the cylinder $\"\"$ , where $\"\"$ is radius and height $\"\"$ .

$\"\"$

Solve the above equation for $\"\"$ .

$\"\"$

$\"\"$ .

Find the equation for the volume of the drinking glass.

Formula for the volume of a cylinder is $\"\"$ , where $\"\"$ is radius and height $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

Find the maximum point by using graph.

Graph the equation $\"\"$ and locate the maximum point.

$\"\"$

Observe the graph:

The maximum point is at $\"\"$ .

Radius of the drinking glass is $\"\"$ inches.

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Height of the drinking glass is $\"\"$ inches.

$\"\"$ inches and $\"\"$ inches.