A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i. e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for ''pi symbol'' and “r^2”.

The change in the cone produces a greater increase in volume.

Step-by-step explanation:

Let's start with the cone.

        (In your case, you would type V = 1/3pi3r^2h/2)

The changes that occurred are and . When we add these together we get .

Now the cylinder.

        (In your case, you would type V = pir^2 2h)

The change that occurred is .

is greater than which means that the change in the cone produces a greater increase in volume.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.