find the surface area of the cylinder in terms of pi
3cm
8cm
To find the surface area of a cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
1. Calculate the area of the two circular bases:
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
Given that the radius of the cylinder is 3 cm, the area of one circular base is:
A = π(3 cm)^2
A = 9π cm^2
Since there are two circular bases, the total area of the two circular bases is:
Total area of two circular bases = 2 * 9π cm^2
Total area of two circular bases = 18π cm^2
2. Calculate the lateral surface area:
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius of the cylinder and h is the height of the cylinder.
Given that the radius of the cylinder is 3 cm and the height is 8 cm, the lateral surface area is:
A = 2π(3 cm)(8 cm)
A = 48π cm^2
3. Add the total area of the two circular bases and the lateral surface area to find the total surface area:
Total surface area = Total area of two circular bases + Lateral surface area
Total surface area = 18π cm^2 + 48π cm^2
Total surface area = 66π cm^2
Therefore, the surface area of the cylinder in terms of π is 66π cm^2.