Ask a New Question
Menu

Find the surface area of the cylinder below. Use the approximation 3.14 for pi.

(1 point)
Responses

1,099 square centimeters
1,099 square centimeters

628 centimeters
628 centimeters

628 square centimeters
628 square centimeters

533.8 square centimeters .

5 answers

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

Since you haven't provided the values for the radius and height, I can't calculate the exact surface area. However, assuming hypothetical values for \( r \) and \( h \), you can substitute them into the formula using \( \pi \approx 3.14 \).

Let's say, for example, the radius (\( r \)) is 10 cm and the height (\( h \)) is 5 cm:

  1. Calculate the surface area: \[ \text{Surface Area} = 2 \times 3.14 \times 10 \times (5 + 10) \] \[ \text{Surface Area} = 2 \times 3.14 \times 10 \times 15 \] \[ \text{Surface Area} = 2 \times 3.14 \times 150 \] \[ \text{Surface Area} = 942 \text{ square centimeters} \]

You can adjust the values for radius and height based on your specific example.

If you provide the radius and height of the cylinder, I would be able to calculate the surface area for you directly. However, based on your answer choices, you can check your calculated values against:

  • 1,099 square centimeters
  • 628 centimeters
  • 628 square centimeters
  • 533.8 square centimeters

Once you have the correct measurements, please calculate again, and see which of the options matches your calculation.

15 cm and 5cm

Given that the radius \( r = 15 \) cm and the height \( h = 5 \) cm, we can use the surface area formula for a cylinder:

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

Substituting \( \pi \approx 3.14 \):

\[ \text{Surface Area} = 2 \times 3.14 \times 15 \times (5 + 15) \] \[ = 2 \times 3.14 \times 15 \times 20 \] \[ = 2 \times 3.14 \times 300 \] \[ = 6.28 \times 300 \] \[ = 1884 \text{ square centimeters} \]

It looks like I miscalculated in the last response—sorry about the confusion. Based on the radius of 15 cm and a height of 5 cm, we find the surface area to be:

\[ \text{Surface Area} = 1884 \text{ square centimeters} \]

This is not among the answer choices you provided earlier. Let's clarify the calculation to ensure it matches:

  1. Lateral surface area: \[ \text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 15 \times 5 = 471 \text{ square centimeters} \]

  2. Top and bottom areas (2 disks): \[ \text{Area of two bases} = 2\pi r^2 = 2 \times 3.14 \times 15^2 = 2 \times 3.14 \times 225 = 1413 \text{ square centimeters} \]

  3. Total surface area: \[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of two bases} = 471 + 1413 = 1884 \text{ square centimeters} \]

Since your answer choices were:

  • 1,099 square centimeters
  • 628 centimeters
  • 628 square centimeters
  • 533.8 square centimeters

It appears that none of these options match the calculated surface area of 1884 square centimeters based on the dimensions you provided. Please verify if there was an error in the dimensions or if there are alternative options available.

15 cm is the H and 5cm is the R

Thank you for clarifying that the height \( h = 15 \) cm and the radius \( r = 5 \) cm. Now we can calculate the surface area of the cylinder again using the correct values.

The formula for the surface area of a cylinder is:

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

Substituting \( r = 5 \) cm and \( h = 15 \) cm, and using \( \pi \approx 3.14 \):

\[ \text{Surface Area} = 2 \times 3.14 \times 5 \times (15 + 5) \] \[ = 2 \times 3.14 \times 5 \times 20 \] \[ = 2 \times 3.14 \times 100 \] \[ = 6.28 \times 100 \] \[ = 628 \text{ square centimeters} \]

Thus, the surface area of the cylinder is 628 square centimeters.

Among your response options, the correct one is:

628 square centimeters.