find the surface area of the cylinder below. height 15cm, with 5cm
To find the surface area of a cylinder, we need to calculate the areas of the two bases and the lateral surface area.
First, let's find the area of one base (which is a circle). The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
Given the radius of 5 cm, we can calculate the area of one base: A = π(5 cm)^2 = 25π cm^2.
Since there are two bases in a cylinder, the total area of the two bases combined is:
2 × 25π cm^2 = 50π cm^2.
Next, let's calculate the lateral surface area. The formula for the lateral surface area of a cylinder is A = 2πrh, where A is the lateral surface area, r is the radius, and h is the height.
Given the radius of 5 cm and the height of 15 cm, we can calculate the lateral surface area: A = 2π(5 cm)(15 cm) = 150π cm^2.
Finally, to find the total surface area, we add the area of the bases and the lateral surface area:
Total surface area = 50π cm^2 + 150π cm^2 = 200π cm^2.
The surface area of the cylinder is 200π cm^2.