Find the surface area of the cylinder below. Use the approximation 3.14 for pi. The height is 15 cm and the length is 5 cm
To find the surface area of the cylinder, we need to find the lateral area and the two bases.
The lateral area of a cylinder is found by multiplying the height by the circumference of the base. The circumference of a circle is found by multiplying the diameter by π. Since the length of the cylinder is given as 5 cm, the diameter of the base is also 5 cm. Therefore, the circumference of the base is 5 cm x 3.14 ≈ 15.7 cm.
The lateral area of the cylinder is the product of the height and the circumference of the base, so the lateral area is 15 cm x 15.7 cm ≈ 235.5 cm^2.
The area of one base of the cylinder is given by the formula A = πr^2, where r is the radius of the base. In this case, the radius is half the diameter, so it is 5 cm / 2 = 2.5 cm. Therefore, the area of one base is 3.14 x (2.5 cm)^2 ≈ 19.625 cm^2.
Since there are two bases, the total area of the two bases is 2 x 19.625 cm^2 = 39.25 cm^2.
Therefore, the total surface area of the cylinder is the sum of the lateral area and the area of the two bases: 235.5 cm^2 + 39.25 cm^2 = 274.75 cm^2.
The surface area of the cylinder is approximately 274.75 cm^2.