Question

1. a right circular cylinder has a radius of 2 centimeters and a height of 4 centimeters, as shown. find the surface area of the right circular cylinder.

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a right - circular cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. With $r = 2$ cm, the area of two bases is $2\pi r^{2}=2\pi\times(2)^{2}=2\pi\times4 = 8\pi$ square centimeters.

Step3: Calculate the lateral - surface area

The lateral - surface area formula is $A_{lateral}=2\pi rh$. Substitute $r = 2$ cm and $h = 4$ cm, we get $2\pi\times2\times4=16\pi$ square centimeters.

Step4: Calculate the total surface area

Add the area of the two bases and the lateral - surface area: $S=2\pi r^{2}+2\pi rh=8\pi + 16\pi=24\pi$ square centimeters. Taking $\pi\approx3.14$, $S\approx24\times3.14 = 75.36$ square centimeters.

Answer:

$24\pi\approx75.36$ square centimeters