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Determine the surface area of the figure through.

Mathematics

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Answer

5600.57 m25600.57 \text{ m}^2

Step-by-step solution

4 steps
  1. Identify the dimensions of the cylinder.

    From the figure, the height (hh) of the cylinder is 70 m and the diameter (dd) of the base is 22 m.

  2. Calculate the radius of the base.

    The radius (rr) is half of the diameter:

    r=d2=22 m2=11 mr = \frac{d}{2} = \frac{22 \text{ m}}{2} = 11 \text{ m}
  3. Apply the formula for the total surface area of a cylinder.

    The total surface area (AA) of a closed cylinder is given by the formula:

    A=2πr2+2πrhA = 2\pi r^2 + 2\pi rh

    where 2πr22\pi r^2 is the area of the two circular bases and 2πrh2\pi rh is the lateral surface area.

  4. Substitute the values and calculate the surface area.

    Using π≈227\pi \approx \frac{22}{7}:

    A=2×227×(11 m)2+2×227×(11 m)×(70 m)A = 2 \times \frac{22}{7} \times (11 \text{ m})^2 + 2 \times \frac{22}{7} \times (11 \text{ m}) \times (70 \text{ m}) A=2×227×121 m2+2×227×11 m×70 mA = 2 \times \frac{22}{7} \times 121 \text{ m}^2 + 2 \times \frac{22}{7} \times 11 \text{ m} \times 70 \text{ m} A=53247 m2+338807 m2A = \frac{5324}{7} \text{ m}^2 + \frac{33880}{7} \text{ m}^2 A=5324+338807 m2A = \frac{5324 + 33880}{7} \text{ m}^2 A=392047 m2A = \frac{39204}{7} \text{ m}^2 A≈5600.57 m2A \approx 5600.57 \text{ m}^2

    The surface area of the cylinder is approximately 5600.57 m25600.57 \text{ m}^2.

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