Final answer:
To calculate the volume of a cylinder with a radius of 2 cm and a height of 6.5 inches (converted to 16.51 cm), we use the formula V = πr²h resulting in a volume of approximately 207.92 cm³.
Step-by-step explanation:
Calculating the Volume of a Cylinder
The student is asking how to find the volume of a cylinder. The given information includes the total surface area of the cylinder, which is 220 cm2, its height of 6.5 inches (which needs to be converted to centimeters), and the radius of 2. To find the volume, we use the formula V = πr²h where V is the volume, r is the radius, and h is the height.
First, we must convert the height from inches to centimeters: 6.5 inches × 2.54 cm/inch = 16.51 cm. Plugging the height and the given radius into the formula, we get:
V = π × (2 cm)² × 16.51 cm
V = π × 4 cm² × 16.51 cm
V = π × 66.04 cm³
Using 3.142 as the approximate value for π:
V = 3.142 × 66.04 cm³
V = 207.91608 cm³
Therefore, the volume of the cylinder is approximately 207.92 cm³.