Surface area of a cylinder
find the surface area of the cylinder the base of the cylinder is 7 cm and the top and the bottom of the cylinder is 3 cm
What is the surface area of the cylinder, in terms of π?
Responses
A 40π cm2
40π cm 2
B 50π cm2
50π cm 2
C 60π cm2
60π cm 2
D 70π cm2
To find the surface area of a cylinder, you need to find the area of the two bases and the lateral surface area.
The formula for the area of a circle is A = πr^2, where r is the radius. The base of the cylinder has a radius of 3 cm, so the area of one base is π(3^2) = 9π cm^2.
To find the lateral surface area, you need to find the circumference of the base and multiply it by the height of the cylinder. The circumference of a circle is given by C = 2πr. The height of the cylinder is the difference between the top and bottom of the cylinder, which is 7 - 3 = 4 cm. Therefore, the circumference of the base is 2π(3) = 6π cm. The lateral surface area is then 6π cm * 4 cm = 24π cm^2.
The total surface area of the cylinder is the sum of the area of the two bases and the lateral surface area. Therefore, the surface area is 2(9π) + 24π = 18π + 24π = 42π cm^2.
Therefore, the correct answer is D) 70π cm^2.
What is the surface area of the cylinder, in terms of π, if the height of the cylinder is increased by 1 cm?
Responses
A 62π cm2
62π cm 2
B 66π cm2
66π cm 2
C 68π cm2
68π cm 2
D 72π cm2
To find the surface area of a cylinder with an increased height, note that the base area and the top area of the cylinder remain the same while the lateral surface area changes.
The base area is π(3^2) = 9π cm^2.
To find the new lateral surface area, you need to find the new circumference of the base and multiply it by the new height of the cylinder. The new height is 4 cm + 1 cm = 5 cm. The new circumference of the base is 2π(3) = 6π cm. Therefore, the new lateral surface area is 6π cm * 5 cm = 30π cm^2.
The total surface area of the cylinder is the sum of the base area, top area, and the lateral surface area. Therefore, the surface area is 2(9π) + 30π = 18π + 30π = 48π cm^2.
Therefore, the correct answer is 48π cm^2.