The net of a cylinder is shown.3cm , 7cm and 3cm
What is the surface area of the cylinder, in terms of π?
Responses
A 40π
40π cm 2
B 50π
50π cm 2
C 60π
60π cm 2
D 70π
To find the surface area of a cylinder, we need to find the area of the two circular bases and the area of the lateral surface.
The area of a circle is given by A = πr^2, where r is the radius.
The radius of the circular bases can be found by dividing the diameter by 2. Therefore, the radius of the circular bases is 3cm / 2 = 1.5cm.
The area of each base is A = π(1.5cm)^2 = 7.07π cm^2.
The lateral surface is a rectangle that wraps around the circular bases. It can be found by finding the perimeter of one circular base and multiplying it by the height of the cylinder. The height of the cylinder is given as 7cm.
The perimeter of a circle is given by P = 2πr. Therefore, the perimeter of one circular base is P = 2π(1.5cm) = 9.42cm.
The lateral surface area is then given by A = P * height = 9.42cm * 7cm = 65.94 cm^2.
To find the total surface area, we add the areas of the two circular bases and the lateral surface area:
Total surface area = 2 * base area + lateral surface area
= 2 * 7.07π cm^2 + 65.94 cm^2
= 14.14π cm^2 + 65.94 cm^2
= 80.08π cm^2
Therefore, the surface area of the cylinder is 80.08π cm^2.
None of the given options match the correct answer of 80.08π cm^2.