The lateral area of the cylinder is 24π units²
Step-by-step explanation:
The lateral area of a cylinder = perimeter of the base × its height
1. The base of the cylinder is a circle
2. The circumference of the circle is 2πr, where r is its radius
3. Area of the circle is πr²
We have the area of the base but we need the circumference, so we
must use the area to find the radius if the base
∵ The area of the circular base of a cylinder = 36π units²
∵ Area of the circle = πr²
∴ 36π = πr²
- Divide both sides by π
∴ 36 = r²
- Take √ for both sides
∴ r = 6 units
Now let us find the circumference of the base
∵ The circumference = 2πr
∵ r = 6 units
∴ The circumference = 2π(6) = 12π units
∵ The lateral area of a cylinder = perimeter of the base × its height
∵ Perimeter of the base is the circumference
∴ Perimeter of the base = 12π
∵ The height of the cylinder is 2 units
∴ The lateral area of a cylinder = 12π × 2
∴ The lateral area of a cylinder = 24π units²
The lateral area of the cylinder is 24π units²
Learn more:
You can learn more about lateral area in brainly.com/question/13005855
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