Find the surface area of a cylinder witth a diameter of 12 inches and a height of 10 inches use the aproximation of 3.14 for pi

1 answer

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

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

where:

  • \( r \) is the radius of the cylinder,
  • \( h \) is the height of the cylinder.

Given:

  • The diameter of the cylinder is 12 inches, so the radius \( r \) is half of that:

\[ r = \frac{12}{2} = 6 \text{ inches} \]

  • The height \( h \) is given as 10 inches.

Substituting these values into the surface area formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 6 \times (10 + 6) \]

Calculating inside the parentheses first:

\[ 10 + 6 = 16 \]

Now substituting back into the formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 6 \times 16 \]

Now calculating \( 2 \times 6 = 12 \):

\[ \text{Surface Area} = 12 \times 3.14 \times 16 \]

Now calculating \( 12 \times 16 = 192 \):

\[ \text{Surface Area} = 192 \times 3.14 \]

Now multiplying \( 192 \times 3.14 \):

\[ \text{Surface Area} \approx 602.88 \text{ square inches} \]

Thus, the surface area of the cylinder is approximately 602.88 square inches.