3 cm 7 cm 3 cm
The net of a cylinder is shown
what is the surface area of the cylinder, in terms of π?
a 40π cm^2
b 50π cm^2
c 60π cm^2
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?
a 62π cm^2
b 66π cm^2
c 68π cm^2
d 72π cm^2
The surface area of a cylinder is calculated by finding the area of the two bases (which are circles) and the lateral surface area (which is the curved surface of the cylinder).
First, let's find the area of the bases. The diameter of the bases is 3 cm, so the radius is 3/2 = 1.5 cm. Therefore, the area of one base is π(radius^2) = π(1.5^2) = 2.25π cm^2.
Since there are two bases, the total area of the bases is 2(2.25π) = 4.5π cm^2.
Next, let's find the lateral surface area. The height of the cylinder is 7 cm, and the circumference of the base is 2π(radius) = 2π(1.5) = 3π cm. Therefore, the lateral surface area is the height multiplied by the circumference, which is 7(3π) = 21π cm^2.
Finally, to find the total surface area, we add the area of the bases to the lateral surface area. Total surface area = 4.5π + 21π = 25.5π cm^2.
Therefore, the surface area of the cylinder in terms of π is 25.5π cm^2.
If the height of the cylinder is increased by 1 cm, the new height becomes 7 + 1 = 8 cm.
Using the same calculations as before, the area of the bases remains the same as 4.5π cm^2.
However, the lateral surface area will change since the height is different. The new lateral surface area is 8(3π) = 24π cm^2.
Therefore, the new total surface area is 4.5π + 24π = 28.5π cm^2.
Therefore, the surface area of the cylinder in terms of π, if the height is increased by 1 cm, is 28.5π cm^2.
The correct answers are:
- For the first question: c) 60π cm^2.
- For the second question: d) 72π cm^2.