Final answer:
To calculate the volume of a solid using the disk method, multiply π by the square of the radius and the height of the cylindrical shape. The example provided used a radius of 0.750 cm and a height of 5.25 cm resulting in a volume of 9.278 cm³. Consistent units are crucial for the accuracy of these calculations.
Step-by-step explanation:
Calculating the Volume of a Solid Using the Disk Method
To calculate the volume of a solid using the disk method, we apply the formula V = πr²h, where V is the volume, r is the radius of the disk, and h is the height of the solid if it's a cylinder. When calculating the volume of a cylinder-shaped object, we can use a calculator to multiply the constant pi (π, approximately 3.142), the square of the radius (r²), and the height (h) to find the volume. For example, given a cylinder with a radius of 0.750 cm and a height of 5.25 cm, we calculate the volume as follows: V = π × (0.750 cm)² × 5.25 cm = 9.278 cm³.
When using the disk method, it's essential to use consistent units throughout the calculation, such as centimeters or meters. This method simplifies the calculation of volumes for solids of revolution by breaking them down into a series of disks with infinitesimal thickness.