The lateral surface area of a cylinder with a height of 12 meters and a diameter of 14 meters is __________

answers:

307.88 sq. meters

527.79 sq. meters

1055.58 sq. meters

1 answer

The lateral surface area \( A_L \) of a cylinder can be calculated using the formula:

\[ A_L = 2 \pi r h \]

where:

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

Given:

  • The diameter of the cylinder is 14 meters, so the radius \( r \) is half of that:

\[ r = \frac{14}{2} = 7 \text{ meters} \]

  • The height \( h \) is given as 12 meters.

Now, substituting the values into the formula:

\[ A_L = 2 \pi (7) (12) \] \[ A_L = 2 \pi \times 7 \times 12 \] \[ A_L = 168 \pi \text{ square meters} \]

Using the approximate value of \( \pi \approx 3.14 \):

\[ A_L \approx 168 \times 3.14 \approx 526.32 \text{ square meters} \]

The closest answer from the given options is:

527.79 sq. meters.

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