Find the surface area of a cylinder with a radius of 4 and a height of 3. Use 3.14 for π

top 4 mm
the side 3mm
(1 point)
Responses

709.89 mm2
709.89 mm 2

175.84 mm2
175.84 mm 2

100.48 mm2
100.48 mm 2

75.36 mm2

1 answer

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

\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]

where:

  • \( r \) is the radius
  • \( h \) is the height
  • The first term, \( 2\pi r^2 \), represents the area of the two circular bases.
  • The second term, \( 2\pi rh \), represents the lateral surface area.

Given:

  • Radius \( r = 4 \) mm
  • Height \( h = 3 \) mm
  • Use \( \pi = 3.14 \)

Now, let's calculate the surface area step by step.

  1. Calculate the area of the two bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 \text{ mm}^2 \]

  2. Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 3 = 2 \times 3.14 \times 12 = 75.36 \text{ mm}^2 \]

  3. Add both areas together: \[ \text{Surface Area} = 100.48 + 75.36 = 175.84 \text{ mm}^2 \]

Therefore, the surface area of the cylinder is 175.84 mm².