Final answer:
The lateral area of a cylinder with a radius of 3 cm and a height of 8 cm is calculated using the formula A = 2πrh, resulting in a lateral area of 150.72π cm².
Step-by-step explanation:
The question asks us to find the lateral area of a cylinder with a radius of 3 cm and a height of 8 cm.
The lateral area of a cylinder can be calculated using the formula for the surface area of a rectangle, which is height times width. For a cylinder, the width is the circumference of the base.
Therefore, the formula for the lateral area (A) of a cylinder is A = 2πrh, where r is the radius and h is the height.
Using the formula:
A = 2π × 3 cm × 8 cm
A = 2 × 3.1415927... × 3 cm × 8 cm
A = 2 × 3.14 × 3 cm × 8 cm
A = 150.72 cm²
When the circumference is calculated as 2πr, the result is a length in centimeters which is then multiplied by the height to find the lateral area. The lateral area of the cylinder is 150.72π cm².