Question

find the surface area of a can of soda. the radius of the base is 4 cm and the height is 13 cm. the can is a cylinder shape. round your answer to the nearest whole number.

Explanation:

Step1: Recall surface - area formula for cylinder

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

Step2: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. With $r = 4$ cm, $A_{base}=\pi\times4^{2}=16\pi$ cm². The area of two bases is $2A_{base}=2\times16\pi = 32\pi$ cm².

Step3: Calculate the lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Substitute $r = 4$ cm and $h = 13$ cm, we get $A_{lateral}=2\pi\times4\times13=104\pi$ cm².

Step4: Calculate the total surface area

$S=2\pi r^{2}+2\pi rh=32\pi + 104\pi=136\pi$ cm².

Step5: Approximate the value

Using $\pi\approx3.14$, $S\approx136\times3.14 = 427.04$ cm². Rounding to the nearest whole number, $S\approx427$ cm².

Answer:

427