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Find the surface area of a cylinder with a base radius of 3 inches and a height of 6 inches.

Write your answer in terms of [tex]\(\pi\)[/tex], and be sure to include the correct unit.

Base radius: 3 in
Height: 6 in


Sagot :

To find the surface area of a cylinder, you can use the surface area formula for a cylinder:

[tex]\[ \text{Surface Area} = 2\pi r(h + r) \][/tex]

where [tex]\( r \)[/tex] is the base radius, and [tex]\( h \)[/tex] is the height of the cylinder.

Given:
- The base radius [tex]\( r \)[/tex] is 3 inches.
- The height [tex]\( h \)[/tex] is 6 inches.

Let's substitute the given values into the formula and simplify step-by-step:

1. Identify [tex]\( r \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ r = 3 \text{ in}, \quad h = 6 \text{ in} \][/tex]

2. Substitute [tex]\( r \)[/tex] and [tex]\( h \)[/tex] into the surface area formula:
[tex]\[ \text{Surface Area} = 2\pi (3) \left(6 + 3\right) \][/tex]

3. Simplify inside the parenthesis first:
[tex]\[ 6 + 3 = 9 \][/tex]

4. Now substitute this value back into the formula:
[tex]\[ \text{Surface Area} = 2\pi (3) \times 9 \][/tex]

5. Multiply 3 by 9:
[tex]\[ 3 \times 9 = 27 \][/tex]

6. Now substitute this value back into the formula:
[tex]\[ \text{Surface Area} = 2\pi \times 27 \][/tex]

7. Finally, multiply 2 by 27:
[tex]\[ 2 \times 27 = 54 \][/tex]

8. Thus, the surface area in terms of [tex]\(\pi\)[/tex] is:
[tex]\[ \text{Surface Area} = 54\pi \text{ square inches} \][/tex]

Therefore, the surface area of the cylinder is:
[tex]\[ 54\pi \text{ square inches} \][/tex]