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Find the surface area of a cylinder with a base radius of 4 m and a height of 6 m. Write your answer in terms of [tex] \pi [/tex], and be sure to include the correct unit.

Base radius: 4 m
Height: 6 m

Sagot :

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To determine the surface area of a cylinder with a base radius of 4 meters and a height of 6 meters, follow these steps:

1. Calculate the area of the two circular bases:
- The formula for the area of a circle is [tex]\(A = \pi \cdot r^2\)[/tex], where [tex]\(r\)[/tex] is the radius.
- Given the radius [tex]\(r = 4\)[/tex] meters, the area of one base is [tex]\( \pi \cdot 4^2 = 16\pi \)[/tex] square meters.
- Since the cylinder has two bases, the total area of the bases is [tex]\( 2 \cdot 16\pi = 32\pi \)[/tex] square meters.

2. Calculate the lateral surface area (the area of the side):
- The formula for the lateral surface area of a cylinder is [tex]\(A = 2\pi r h\)[/tex], where [tex]\(r\)[/tex] is the radius and [tex]\(h\)[/tex] is the height.
- Given the radius [tex]\(r = 4\)[/tex] meters and the height [tex]\(h = 6\)[/tex] meters, the lateral surface area is [tex]\( 2\pi \cdot 4 \cdot 6 = 48\pi \)[/tex] square meters.

3. Calculate the total surface area:
- The total surface area of the cylinder is the sum of the area of the bases and the lateral surface area.
- Therefore, the total surface area is [tex]\( 32\pi + 48\pi = 80\pi \)[/tex] square meters.

So, the surface area of the cylinder is [tex]\( 80\pi \)[/tex] square meters.
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