Giulia is designing glass storage jars with surface area 675 cm2.The jars are cylinders. She wants to maximize the volume of each jar to save on the materials cost. a) What dimensions should Giulia use? b) What will the volume be?

a) radius: 6.0 cm, height: 11.9 cm

b)

Step-by-step explanation:

a)

The surface area of a cylinder is given by the sum of:

- The area of the two bases, so , where r is the radius of the cylinder

- The lateral area of the cylinder, so , where h is the height of the cylinder

So the surface area can be written as

Re-arranging the equation, we can rewrite it making h the subject:

(1)

The volume of the cylinder instead is given by

By substituting (1) into this expression, we find:

Here we want to maximize the volume of the jar, so we have to require its first derivative to be zero, so:

We also know that the surface area of the jar must be

So, the radius of the cylinder must be

While the height is

b)

The volume of the cylinder is given by:

where

r is the radius of the cylinder

h is the height of the cylinder

In this problem, we have:

r = 6.0 cm is the radius of the jar

h = 11.9 cm is the height of the jar

So, the volume of the jar is

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05