A cylinder has a volume of 48π cm3 and height h. Complete this table for volume of cylinders with the same radius but different heights.

(i) For , the volume is cubic centimeters.

(ii) For , the volume is cubic centimeters.

(iii) For , the volume is cubic centimeters.

(iv) For , the volume is cubic centimeters.

Step-by-step explanation:

The volume of the cylinder (), measured in cubic centimeters, is defined by the following formula:

(1)

Where:

- Radius, measured  in centimeters.

- Height, measured in centimeters.

From statement, we understand that volume of the cylinder is directly proportional to its height. That is:

(2)

Where is the proportionality constant, measured in square centimeters.

In addition, we eliminate this constant by constructing the following relationship:

(3)

Based on (3) and knowing that , we calculate the volumes for each height ratio:

(i) For , the volume is cubic centimeters.

(ii) For , the volume is cubic centimeters.

(iii) For , the volume is cubic centimeters.

(iv) For , the volume is cubic centimeters.

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e