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Find the surface area of a cylinder with a radius of 5 inches and a height of 10 inches u=Use the aproximation 3.14 as pi.

3 answers

To find the surface area of a cylinder, we 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, and
  • \( \pi \) is approximately \( 3.14 \).

Given:

  • \( r = 5 \) inches,
  • \( h = 10 \) inches.

Now plug these values into the formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 5 (10 + 5) \]

Calculating \( h + r \):

\[ h + r = 10 + 5 = 15 \]

Now substitute this back into the formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 5 \times 15 \]

Calculating:

  1. First calculate \( 2 \times 3.14 = 6.28 \).
  2. Then calculate \( 5 \times 15 = 75 \).
  3. Finally, multiply these results together:

\[ \text{Surface Area} = 6.28 \times 75 \]

Calculating \( 6.28 \times 75 \):

\[ 6.28 \times 75 = 471 \]

Thus, the surface area of the cylinder is approximately:

\[ \text{Surface Area} \approx 471 \text{ square inches} \]

you sure-?

Let’s verify the calculations step by step for the surface area of the cylinder to ensure everything is correct.

The formula for the surface area of a cylinder is:

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

where:

  • \( r = 5 \) inches (radius),
  • \( h = 10 \) inches (height),
  • \( \pi \approx 3.14 \).

Step 1: Calculate \( h + r \)

\[ h + r = 10 + 5 = 15 \]

Step 2: Plug the values into the formula

\[ \text{Surface Area} = 2 \times 3.14 \times 5 \times 15 \]

Step 3: Calculate \( 2 \times 3.14 \)

\[ 2 \times 3.14 = 6.28 \]

Step 4: Calculate \( 5 \times 15 \)

\[ 5 \times 15 = 75 \]

Step 5: Now multiply \( 6.28 \times 75 \)

Now let's calculate \( 6.28 \times 75 \):

\[ 6.28 \times 75 = 471 \]

Conclusion

After verifying the calculations, the surface area of the cylinder is indeed approximately:

\[ \text{Surface Area} \approx 471 \text{ square inches} \]

If you have any further questions or need additional clarification, feel free to ask!